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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption 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no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .gtIExW ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .gtIExW ol li{margin:10px 0;padding-left:10px;word-break:normal;} .gtIExW ol li a{word-break:break-all;} .gtIExW ol li .reflinks{display:block;} .gtIExW ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .gtIExW ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .gtIExW ol li .reflinks .sep{color:#000000;} .gtIExW .table-wrapper{width:auto;overflow-x:auto;} .gtIExW .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .gtIExW .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 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height="24"><span class="text">提交</年代pan></span><span class="sc-htoDjs kNoiZu sc-dqBHgY cQgXqt fileArrow icon-colored undefined icon-themeable" title="" font-size="16"></span></a> <div class="sc-krDsej ewCAZX hide__submenu journalSubmenuCheck" id="journalnav__submenu"> <button class="sc-itybZL kdvWPs journalSubmenuCheck"><span class="sc-htoDjs gvAGTV sc-fzsDOv hAFFGk journalSubmenuCheck icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="9"></span></button> </div> <div class="sc-dTdPqK lkWWFY hide__submenu journal__nav__desktop" id="journalnav__submenudesktop"> <div order="0" class="sc-kUaPvJ ehYbwJ"> <div class="sc-gPWkxV legory"></div> <div class="sc-gPWkxV legory"></div> </div> <div class="sc-jVODtj epgILe"></div> <span class="sc-fONwsr kCfRMJ"></span> </div> </nav> </div> <div class="sc-nrwXf byflLi breadcrumb__wrapper journal_article__BreadCrumbStyle-sc-12fk6zy-2 bjwAQR article"> <a class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jcse/" aria-label="Journal of Control Science and Engineering">控制科学与工程》杂志上</一个>/<一个class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jcse/contents/year/2011/" aria-label="2011">2011年</一个>/<年代pan class="sc-bhlBdH UVThf">文章</年代pan> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</button> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在这一页上</p> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#abstract" aria-label="">文摘</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#introduction" aria-label="">介绍</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#examples-and-simulations" aria-label="">例子</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#conclusions" aria-label="">结论</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#references" aria-label="">引用</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#copyright" aria-label="">版权</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#related-articles" aria-label="">相关文章</一个></年代pan> </div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <p class="sc-kZmsYB bkiEfx article_type">研究文章|开放获取</p> <div class="sc-RcBXQ ztvYg article_citation"> 体积 2011年 <span class="sc-fZwumE cUsFHx">|</年代pan>文章的ID 719730年 <span class="sc-fZwumE cUsFHx">|</年代pan> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2011/719730" aria-label="Doi-link">https://doi.org/10.1155/2011/719730</一个></div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>他Shu-An, I-Kong方, ”<年代pan class="adjust-article-svg-size">一阶线性时滞反馈系统的稳定性和性能:一个特征值的方法</年代pan>”,<i>控制科学与工程》杂志上</我>, 卷。2011年, 文章的ID719730年, 8   页面, 2011年。 https://doi.org/10.1155/2011/719730</p> </div> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</button> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN jVSHWt article_title adjust-article-svg-size heading-title">一阶线性时滞反馈系统的稳定性和性能:一个特征值的方法</h1></div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class="">Shu-An他<年代up>1</年代up>和</年代pan> <span class=""><b>I-Kong方</b><一个class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><sup>1</年代up></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</年代up><span>国立台湾大学电机工程系,10617年台北,台湾</年代pan></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</button> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</b>偏向可能性</div> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年4月25日</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年8月26日</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">06年9月2011年</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年12月13日</年代pan> </div> </div> </div> <article class="sc-jtRlXQ gtIExW article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><p>线性时滞系统的先验特征方程有无穷多的特征值通常很难完全计算。然而,一阶线性时滞系统的光谱可以用兰伯特函数进行分析。本文研究了稳定和一阶线性时滞系统的状态反馈稳定通过兰伯特详细功能。有关的主要问题是最右边的特征值位置,稳定鲁棒性对延迟时间,响应闭环系统的性能。例子和仿真给出了说明分析结果。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4><p>系统内部信号传输延迟是很常见的电气、机械、生物、化学工程问题。系统组件的延迟可能是固有的特点或控制过程的一部分<一个href=”#B1">1</一个>]。迟钝型时滞系统探讨属于那些可以由常微分方程建模(常微分方程)结合不同条款,称为微分差分方程(dd) [<一个href=”#B2">2</一个>]。</p> <p>最近,研究工作状态的解决方案,时滞系统的可控性、可观测性和控制器设计是非常丰富的<一个href=”#B3">3</一个>,<一个href=”#B4">4</一个>]。在控制器设计领域,许多文学评论(<一个href=”#B5">5</一个>- - - - - -<一个href=”#B7">7</一个>提出线性矩阵不等式(LMI)条件找到控制器。然而,合成LMI条件大多是足够的。</p> <p>迟钝型时滞系统被认为是无限维的,超越特征方程和一个无限的频谱。在过去的十年里,许多作品来发现的主导特征值甚至整个频谱。例如,在[<一个href=”#B8">8</一个>]介绍了很多方法迭代地找到近似最右面的特征值。另一个重要的数值方法提出了(<一个href=”#B9">9</一个>),它使用兰伯特函数来开发一个频谱的表达式。随后,表达式应用于决定国家的解决方案,讨论可控制性和可观测性,设计状态反馈控制器(<一个href=”#B10">10</一个>- - - - - -<一个href=”#B13">13</一个>]。</p> <p>通过兰伯特函数方法,理论上可以观察到光谱的完整视图。最近,一个辅助矩阵引入结合兰伯特函数寻找高阶时滞系统的光谱,但也指出,这样的辅助矩阵的存在性和唯一性仍开放问题[<一个href=”#B14">14</一个>]。因此,作为复杂的高阶时滞系统的基础,本文讨论了一阶延迟系统集中在兰伯特的功能。</p> <p>一阶线性系统具有输入时滞一直专注的研究在文学评论等(<一个href=”#B8">8</一个>,<一个href=”#B15">15</一个>]。讨论稳定,普遍关心的三个因素的影响:系统参数、控制器增益,和延迟的大小。在[<一个href=”#B15">15</一个>]研究了比例控制器,只有稳定控制器增益的范围进行了分析通过Pade逼近和穿越频率的决心。在[<一个href=”#B8">8</一个>),稳定区域图构造对上述三个因素,但该方法提出在本质上是迭代的计算量。通过兰伯特函数的性质,探讨稳定性以及性能的一阶线性时滞系统的状态反馈。不仅稳定条件,但整个闭环谱可以公开,便于控制器的选择收益实现控制目标。更具体地说,将位于最右边的特征值,并将强调一些更深层次的问题,包括稳定和稳定鲁棒性对延迟时间。此外,如何选择反馈增益为了获得更好的响应性能也覆盖。最后,实例和模拟给出了说明分析结果。</p> <h4 id="problem-formulation">2。问题公式化</h4><p>考虑一阶时滞系统,<年代pan class="equation" id="EEq2.1"> <svg height="41.349998" id="M1" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.35)"> <g transform="translate(72,-38.92)"> <text transform="matrix(1,0,0,-1,127.74,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</t年代pan> <tspan style="font-size: 12.50px; " x="-6.6640992" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="2.2755461" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="6.439045" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.352484" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.991817" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,164.05,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,168.93,63.2)"> <tspan style="font-size: 12.50px; " x="-5.73" y="20.48"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.9521484" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.115647" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.029085" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="23.96825" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.308472" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.184883" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.199306" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="53.362804" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="60.05191" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="71.392128" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="78.618866" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="84.857864" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="100.03651" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="107.41328" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="119.45366" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="125.70516" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="3.23" y="20.469999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.3934989" y="20.469999"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.306938" y="20.469999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.933767" y="20.469999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.974157" y="20.469999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.79,39.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.66,42.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="15.166139" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="34.595802" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="40.847301" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="262.45999" y="-9.6199999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="266.6235" y="-9.6199999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="272.875" y="-9.6199999"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.8875" id="M2" style="vertical-align:-0.33858pt;width:39.787498px;" version="1.1" viewbox="0 0 39.787498 10.8875" width="39.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> ℝ</t年代pan> </text> </g> </g> </svg>是状态变量,<年代vg height="10.8875" id="M3" style="vertical-align:-0.33858pt;width:38.599998px;" version="1.1" viewbox="0 0 38.599998 10.8875" width="38.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3897533" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.430141" y="0"> ℝ</t年代pan> </text> </g> </g> </svg>是输入信号,<年代vg height="14.5375" id="M4" style="vertical-align:-3.25793pt;width:45.125px;" version="1.1" viewbox="0 0 45.125 14.5375" width="45.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5375)"> <g transform="translate(72,-60.37)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> ℝ</t年代pan> </text> </g> </g> </svg>和<年代vg height="10.9875" id="M5" style="vertical-align:-0.33858pt;width:38.537498px;" version="1.1" viewbox="0 0 38.537498 10.9875" width="38.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9875)"> <g transform="translate(72,-63.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3397408" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.380131" y="0"> ℝ</t年代pan> </text> </g> </g> </svg>系统参数,<年代vg height="10.95" id="M6" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>是一个非负常数延迟时间,<年代vg height="11.075" id="M7" style="vertical-align:-3.25793pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 11.075" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>是初始条件。当一个状态反馈控制器<年代vg height="13.45" id="M8" style="vertical-align:-2.21957pt;width:78.025002px;" version="1.1" viewbox="0 0 78.025002 13.45" width="78.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.00336" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="21.63019" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="33.670578" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.197865" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.074516" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="54.238014" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="58.151451" y="0"> )</t年代pan> </text> </g> </g> </svg>应用(<一个href=”#EEq2.1">1</一个>)成为<年代pan class="equation" id="EEq2.2"> <svg height="65.412498" id="M9" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 65.412498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,65.4125)"> <g transform="translate(72,-19.67)"> <text transform="matrix(1,0,0,-1,124.63,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</t年代pan> <tspan style="font-size: 12.50px; " x="-6.6766019" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="2.2755461" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="6.439045" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.352484" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.991817" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,160.94,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,165.81,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.9646511" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.12815" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.04159" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="23.980755" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.320976" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.41,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,212.29,63.2)"> <tspan style="font-size: 12.50px; " x="-18.870001" y="38.549999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-7.54" y="23.6"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.9521484" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.115647" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.804752" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.359203" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="44.610703" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="59.789345" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="67.166115" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="79.206505" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="85.458008" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-55.580002" y="31.219999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-46.627853" y="31.219999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-42.464352" y="31.219999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-38.550915" y="31.219999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-30.911581" y="31.219999"> =</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.63,36.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,216.5,39.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.00552" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="41.297409" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-11.75" y="15"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-5.4984999" y="15"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="15.619067" y="15"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.008341" y="15"> <</t年代pan> <tspan style="font-size: 12.50px; " x="35.048729" y="15"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="41.300228" y="15"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="257.62" y="-3.1099999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="261.78351" y="-3.1099999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="268.035" y="-3.1099999"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.475" id="M10" style="vertical-align:-3.13504pt;width:53.962502px;" version="1.1" viewbox="0 0 53.962502 14.475" width="53.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.9168" y="0"> </t年代pan> </text> </g> </g> </svg>。状态方程模型(<一个href=”#EEq2.2">2</一个>)是一个DDE,系统的稳定性和稳定研究。特征方程(<一个href=”#EEq2.2">2</一个>)是<年代vg height="17.9125" id="M11" style="vertical-align:-3.25793pt;width:144.33749px;" version="1.1" viewbox="0 0 144.33749 17.9125" width="144.33749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.691984" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="26.318815" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="38.359203" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.636189" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="57.97641" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-7.68,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.03,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,17.59,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,22.46,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,28.03,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>一个先验的,有着无穷多的根源。有一些数值方法求解这类方程,比如ODE-based方法(<一个href=”#B16">16</一个>),但利用朗伯函数(<一个href=”#B17">17</一个>)公开属性的特征值。</p> <h4 id="the-lambert-function">3所示。兰伯特函数</h4><p>兰伯特函数<年代vg height="13.625" id="M12" style="vertical-align:-2.21957pt;width:31.85px;" version="1.1" viewbox="0 0 31.85 13.625" width="31.85" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.625)"> <g transform="translate(72,-61.1)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.478234" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="17.641733" y="0"> ⋅</t年代pan> <tspan style="font-size: 12.50px; " x="21.21759" y="0"> )</t年代pan> </text> </g> </g> </svg>是满足的功能<年代vg height="16.6625" id="M13" style="vertical-align:-2.21957pt;width:144.41251px;" version="1.1" viewbox="0 0 144.41251 16.6625" width="144.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6625)"> <g transform="translate(72,-58.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.478234" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="17.641733" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.88073" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="28.04423" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.34,65.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.4346561" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="12.349072" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="16.71632" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.74,60.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.266884" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.644133" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.358963" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="49.399353" y="0"> ℂ</t年代pan> </text> </g> </g> </svg>。它是一个多值函数,函数值和被列为主要分支<年代vg height="10.7375" id="M14" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>th-branch所有非零的整数<年代vg height="10.7375" id="M15" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。表达<年代vg height="13.4875" id="M16" style="vertical-align:-2.34499pt;width:68.574997px;" version="1.1" viewbox="0 0 68.574997 13.4875" width="68.574997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.570074" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="42.910297" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.773964" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="13.7875" id="M17" style="vertical-align:-2.34499pt;width:94.474998px;" version="1.1" viewbox="0 0 94.474998 13.7875" width="94.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7875)"> <g transform="translate(72,-60.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.478234" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="17.641733" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.88073" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="31.507561" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="43.547951" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.012718" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="64.352943" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.216606" y="0"> </t年代pan> </text> </g> </g> </svg>复数的形式,一个有关系<年代pan class="equation" id="EEq3.1"> <svg height="47.825001" id="M18" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 47.825001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,47.825)"> <g transform="translate(72,-33.74)"> <text transform="matrix(1,0,0,-1,145.37,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.527526" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.5,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.77,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.928102" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="18.479433" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="24.730934" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="31.670099" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.709766" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="52.049988" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="60.389488" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="65.253159" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="68.728989" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="77.055992" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="83.307487" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="89.55899" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-35.360001" y="23.57"> </t年代pan> <tspan style="font-size: 12.50px; " x="-24.919994" y="23.57"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-12.879606" y="23.57"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.46,42.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.73,37.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="31.244997" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.272163" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="51.612385" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="60.389488" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="65.253159" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="68.728989" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="77.055992" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="83.307487" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="89.55899" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="293.39001" y="-12.2"> (</t年代pan> <tspan style="font-size: 12.50px; " x="297.5535" y="-12.2"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="303.80499" y="-12.2"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>在下一节中,这将是清楚<年代vg height="10.8875" id="M19" style="vertical-align:-0.33858pt;width:38.987499px;" version="1.1" viewbox="0 0 38.987499 10.8875" width="38.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> ℝ</t年代pan> </text> </g> </g> </svg>需要讨论这篇文章的目的,所以<年代vg height="13.55" id="M20" style="vertical-align:-2.29482pt;width:35.137501px;" version="1.1" viewbox="0 0 35.137501 13.55" width="35.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 0</t年代pan> </text> </g> </g> </svg>或<年代vg height="13.425" id="M21" style="vertical-align:-2.29482pt;width:73.1875px;" version="1.1" viewbox="0 0 73.1875 13.425" width="73.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.75738" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.008881" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="42.560211" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="48.72419" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="52.200024" y="0"> </t年代pan> </text> </g> </g> </svg>与<年代vg height="13.55" id="M22" style="vertical-align:-2.29482pt;width:36.049999px;" version="1.1" viewbox="0 0 36.049999 13.55" width="36.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.480394" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.725" id="M23" style="vertical-align:-2.29482pt;width:62.924999px;" version="1.1" viewbox="0 0 62.924999 13.725" width="62.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.478234" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="17.641733" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.88073" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="31.507561" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="43.547951" y="0"> </t年代pan> </text> </g> </g> </svg>或<年代vg height="13.7875" id="M24" style="vertical-align:-2.34499pt;width:131.425px;" version="1.1" viewbox="0 0 131.425 13.7875" width="131.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7875)"> <g transform="translate(72,-60.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.478234" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="17.641733" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.88073" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="31.507561" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="43.547951" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="52.112503" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="58.364002" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="63.915337" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="70.079315" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="73.555145" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="82.569809" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="93.910034" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="98.773697" y="0"> </t年代pan> </text> </g> </g> </svg><i>。</我>函数的部分情节<年代vg height="13.425" id="M25" style="vertical-align:-2.29482pt;width:73.1875px;" version="1.1" viewbox="0 0 73.1875 13.425" width="73.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.75738" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.008881" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="42.560211" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="48.72419" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="52.200024" y="0"> </t年代pan> </text> </g> </g> </svg>显示在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig1/" target="_blank">1</一个>,很容易推断出其余的部分功能。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="719730.fig.001" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.001.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/719730/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="13.425" id="M26" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 75.787498 13.425" width="75.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.75738" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.008881" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="42.560211" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="48.72419" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="54.275524" y="0"> </t年代pan> </text> </g> </g> </svg> <table> 的情节。</t一个ble> </div> </div> </div> <p>基于图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig1/" target="_blank">1</一个>按照惯例,(<一个href=”#EEq3.2a">4</一个>)以下定义的主要分支<年代vg height="14.925" id="M27" style="vertical-align:-3.25793pt;width:40.412498px;" version="1.1" viewbox="0 0 40.412498 14.925" width="40.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> z</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> )</t年代pan> </text> </g> </g> </svg>兰伯特的函数,(<一个href=”#EEq3.2a">4 b</一个>)定义了−1 st-branch<年代vg height="14.775" id="M28" style="vertical-align:-3.13504pt;width:48.762501px;" version="1.1" viewbox="0 0 48.762501 14.775" width="48.762501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.6,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> </text> </g> </g> </svg>,(<一个href=”#EEq3.2a">4摄氏度</一个>)定义了<年代vg height="10.7375" id="M29" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>th-branch。<年代pan class="equation" id="EEq3.2a"> <svg height="211.96249" id="M30" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 211.96249" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,211.9625)"> <g transform="translate(72,97.57)"> <text transform="matrix(1,0,0,-1,100.91,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,114.38,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,121.34,53.45)"> <tspan style="font-size: 12.50px; " x="30.08" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-62.509998" y="39.73"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="41.41" y="-7.6199999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="49.974556" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="56.213551" y="-7.6199999"> c</t年代pan> <tspan style="font-size: 12.50px; " x="61.764885" y="-7.6199999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="67.928864" y="-7.6199999"> t</t年代pan> <tspan style="font-size: 12.50px; " x="73.480194" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="82.507362" y="-7.6199999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="93.84758" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="98.71125" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="104.96275" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="120.5915" y="-7.6199999"> f</t年代pan> <tspan style="font-size: 12.50px; " x="124.36741" y="-7.6199999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="130.61891" y="-7.6199999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="138.94591" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="148.66074" y="-7.6199999"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="162.78912" y="-7.6199999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="166.95262" y="-7.6199999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="173.20412" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="178.41788" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="186.0197" y="-7.6199999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="192.2587" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.41" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.086601" y="7.3800001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="120.6" y="7.3800001"> f</t年代pan> <tspan style="font-size: 12.50px; " x="124.37591" y="7.3800001"> o</t年代pan> <tspan style="font-size: 12.50px; " x="130.62741" y="7.3800001"> r</t年代pan> <tspan style="font-size: 12.50px; " x="138.94189" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="149.10684" y="7.3800001"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="163.9229" y="7.3800001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="175.26312" y="7.3800001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="181.51462" y="7.3800001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="347.23001" y="-7.1054274e-015"> (</t年代pan> <tspan style="font-size: 12.50px; " x="351.39349" y="-7.1054274e-015"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="357.64499" y="-7.1054274e-015"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="363.19632" y="-7.1054274e-015"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,72.3,10.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,85.26,13.73)"> <tspan style="font-size: 12.50px; " x="30.07" y="7.3400002"> </t年代pan> <tspan style="font-size: 12.50px; " x="-48.529999" y="69.360001"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="41.400002" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.089104" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="120.6" y="-7.6199999"> f</t年代pan> <tspan style="font-size: 12.50px; " x="124.3634" y="-7.6199999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="130.6149" y="-7.6199999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="138.94189" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="149.10684" y="-7.6199999"> <</t年代pan> <tspan style="font-size: 12.50px; " x="161.13472" y="-7.6199999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="169.69928" y="-7.6199999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="175.95078" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.400002" y="7.3899999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="49.964554" y="7.3899999"> </t年代pan> <tspan style="font-size: 12.50px; " x="56.216057" y="7.3899999"> c</t年代pan> <tspan style="font-size: 12.50px; " x="61.767387" y="7.3899999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="67.931366" y="7.3899999"> t</t年代pan> <tspan style="font-size: 12.50px; " x="73.470192" y="7.3899999"> </t年代pan> <tspan style="font-size: 12.50px; " x="82.509865" y="7.3899999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="93.850082" y="7.3899999"> </t年代pan> <tspan style="font-size: 12.50px; " x="98.713753" y="7.3899999"> </t年代pan> <tspan style="font-size: 12.50px; " x="104.96526" y="7.3899999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="120.594" y="7.3899999"> f</t年代pan> <tspan style="font-size: 12.50px; " x="124.36991" y="7.3899999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="130.62141" y="7.3899999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="138.9359" y="7.3899999"> </t年代pan> <tspan style="font-size: 12.50px; " x="148.66324" y="7.3899999"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="162.78999" y="7.3800001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="166.95351" y="7.3800001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="175.51805" y="7.3800001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="181.76955" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="189.37138" y="7.3800001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="194.57263" y="7.3800001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="203.13718" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="210.739" y="7.3800001"> )</t年代pan> <tspan style="font-size: 12.50px; " x="217.67818" y="7.3800001"> ∪</t年代pan> <tspan style="font-size: 12.50px; " x="230.2937" y="7.3800001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="234.4572" y="7.3800001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="243.02174" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="250.62358" y="7.3800001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="255.83733" y="7.3800001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="262.08884" y="7.3800001"> )</t年代pan> <tspan style="font-size: 12.50px; " x="268.34033" y="7.3800001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="382.60999" y="0.0099999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="386.7735" y="0.0099999998"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="393.02499" y="0.0099999998"> b</t年代pan> <tspan style="font-size: 12.50px; " x="399.27649" y="0.0099999998"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,50.2,-58.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,57.53,-55.63)"> <tspan style="font-size: 12.50px; " x="33.07" y="-33.080002"> ⎧</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="-27.530001"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="-17.290001"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="-7.0500002"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="3.1900001"> ⎨</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="13.43"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="23.68"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="33.919998"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="33.07" y="39.400002"> ⎩</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="41.07" y="-37.630001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="49.634556" y="-37.630001"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.87355" y="-37.630001"> c</t年代pan> <tspan style="font-size: 12.50px; " x="61.424885" y="-37.630001"> o</t年代pan> <tspan style="font-size: 12.50px; " x="67.58886" y="-37.630001"> t</t年代pan> <tspan style="font-size: 12.50px; " x="71.064697" y="-37.630001"> </t年代pan> <tspan style="font-size: 12.50px; " x="80.091866" y="-37.630001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="91.432083" y="-37.630001"> </t年代pan> <tspan style="font-size: 12.50px; " x="96.295753" y="-37.630001"> </t年代pan> <tspan style="font-size: 12.50px; " x="102.54725" y="-37.630001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.07" y="-22.629999"> f</t年代pan> <tspan style="font-size: 12.50px; " x="44.833405" y="-22.629999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="51.084904" y="-22.629999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="59.4119" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.126732" y="-22.629999"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="83.255119" y="-22.629999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="87.418617" y="-22.629999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="91.582123" y="-22.629999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="97.833618" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="107.38591" y="-22.629999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="118.72614" y="-22.629999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="124.97763" y="-22.629999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="131.22913" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="138.83096" y="-22.629999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="144.04471" y="-22.629999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="150.2962" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="157.07283" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="164.67465" y="-22.629999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="171.61383" y="-22.629999"> ∪</t年代pan> <tspan style="font-size: 12.50px; " x="184.22935" y="-22.629999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="188.39285" y="-22.629999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="194.64435" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="201.42097" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="209.0228" y="-22.629999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="214.22404" y="-22.629999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="218.38754" y="-22.629999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="224.63905" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="234.20384" y="-22.629999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="245.54407" y="-22.629999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="251.79556" y="-22.629999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="258.04706" y="-22.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="265.6489" y="-22.629999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="271.88788" y="-22.629999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="170.58" y="-7.6199999"> </t年代pan> <tspan style="font-size: 12.50px; " x="180.81996" y="-7.6199999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="192.86035" y="-7.6199999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="199.11185" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="204.32559" y="-7.6199999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="210.5771" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="215.79085" y="-7.6199999"> …</t年代pan> <tspan style="font-size: 12.50px; " x="230.36934" y="-7.6199999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.07" y="7.3800001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="49.634556" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.87355" y="7.3800001"> c</t年代pan> <tspan style="font-size: 12.50px; " x="61.424885" y="7.3800001"> o</t年代pan> <tspan style="font-size: 12.50px; " x="67.58886" y="7.3800001"> t</t年代pan> <tspan style="font-size: 12.50px; " x="71.064697" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="80.091866" y="7.3800001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="91.432083" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="96.295753" y="7.3800001"> </t年代pan> <tspan style="font-size: 12.50px; " x="102.54725" y="7.3800001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.07" y="22.389999"> f</t年代pan> <tspan style="font-size: 12.50px; " x="44.833405" y="22.389999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="51.084904" y="22.389999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="59.4119" y="22.389999"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.126732" y="22.389999"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="83.260002" y="22.379999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="87.4235" y="22.379999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="93.674995" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="100.45162" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="108.04095" y="22.379999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="113.2547" y="22.379999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="117.4182" y="22.379999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="123.66969" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="133.22198" y="22.379999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="144.57471" y="22.379999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="150.82622" y="22.379999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="157.06522" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="164.66704" y="22.379999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="171.6062" y="22.379999"> ∪</t年代pan> <tspan style="font-size: 12.50px; " x="184.22173" y="22.379999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="188.38522" y="22.379999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="192.54872" y="22.379999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="198.80022" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="208.36502" y="22.379999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="219.70525" y="22.379999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="225.95674" y="22.379999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="232.20824" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="239.81006" y="22.379999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="245.01131" y="22.379999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="253.35081" y="22.379999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="257.51431" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="267.06659" y="22.379999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="278.40683" y="22.379999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="284.65833" y="22.379999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="290.90982" y="22.379999"> </t年代pan> <tspan style="font-size: 12.50px; " x="298.51166" y="22.379999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="304.76315" y="22.379999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="170.58" y="37.389999"> </t年代pan> <tspan style="font-size: 12.50px; " x="180.81996" y="37.389999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="192.86035" y="37.389999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="201.4249" y="37.389999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="207.67641" y="37.389999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="212.89015" y="37.389999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="221.45471" y="37.389999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="227.70621" y="37.389999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="232.91995" y="37.389999"> …</t年代pan> <tspan style="font-size: 12.50px; " x="247.49846" y="37.389999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="411.04001" y="-1.4210855e-014"> (</t年代pan> <tspan style="font-size: 12.50px; " x="415.20349" y="-1.4210855e-014"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="421.45499" y="-1.4210855e-014"> c</t年代pan> <tspan style="font-size: 12.50px; " x="427.00632" y="-1.4210855e-014"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>兰伯特的几个分支功能策划,每一个都有不同的颜色,和的值<年代vg height="13.45" id="M33" style="vertical-align:-2.21957pt;width:112.0875px;" version="1.1" viewbox="0 0 112.0875 13.45" width="112.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.270245" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="44.310631" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="48.474133" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="57.038685" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="68.616463" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="73.817711" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="85.395493" y="0"> )</t年代pan> </text> </g> </g> </svg>与黑色字体标记在相应的位置。从图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>可以得出很多结论,包括以下两个前题。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="719730.fig.002" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.002.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/719730/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="7.375" id="M34" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 36.125 7.375" width="36.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.375)"> <g transform="translate(72,-66.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </t年代pan> </text> </g> </g> </svg> <table> 兰伯特的几个分支函数参数化的值。</t一个ble> </div> </div> </div> <p><span class="statement" id="lem1"><span class="statement-title">引理1。</年代pan><i>只有部分的<年代vg height="14.925" id="M35" style="vertical-align:-3.25793pt;width:41.275002px;" version="1.1" viewbox="0 0 41.275002 14.925" width="41.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.775" id="M36" style="vertical-align:-3.13504pt;width:48.762501px;" version="1.1" viewbox="0 0 48.762501 14.775" width="48.762501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.6,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> </text> </g> </g> </svg>实值,和所有其他分支的兰伯特是复值函数。</我><br><我>事实上,只有<年代vg height="14.925" id="M37" style="vertical-align:-3.25793pt;width:68.487503px;" version="1.1" viewbox="0 0 68.487503 14.925" width="68.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> 0</t年代pan> </text> </g> </g> </svg>,和所有其他分支是未定义的<年代vg height="10.9125" id="M38" style="vertical-align:-0.17555pt;width:35.125px;" version="1.1" viewbox="0 0 35.125 10.9125" width="35.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> 0</t年代pan> </text> </g> </g> </svg>。同时,</我><年代pan class="equation" id="EEq3.3a"> <svg height="116.3125" id="M39" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 116.3125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,116.3125)"> <g transform="translate(72,21.05)"> <text transform="matrix(1,0,0,-1,99.31,54.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,112.79,51.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,125.74,54.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.069715" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.29,59.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.45,54.45)"> <tspan style="font-size: 12.50px; " x="77.900002" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="16.641493" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="35.708569" y="0"> f</t年代pan> <tspan style="font-size: 12.50px; " x="39.484474" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="45.735973" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="54.062973" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="63.765301" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="83.75" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="92.314552" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="103.89233" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="109.09358" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="117.65813" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,299.68,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,310.55,51.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="-231.8" y="31.459999"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.8400002" y="-4.3899999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="158.02" y="-4.3899999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="162.1835" y="-4.3899999"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="168.435" y="-4.3899999"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="173.98633" y="-4.3899999"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,92.23,17.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,99.56,20.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.069715" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,143.11,25.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,156.43,20.48)"> <tspan style="font-size: 12.50px; " x="-87.449997" y="33.98"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="16.653996" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="35.708569" y="0"> f</t年代pan> <tspan style="font-size: 12.50px; " x="39.484474" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="45.735973" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="54.062973" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="63.777802" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="77.893692" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="82.05719" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="88.308685" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="93.522438" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="105.10022" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="111.33922" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="118.64097" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="128.88092" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="140.92131" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="147.17281" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="152.38657" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="158.63806" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="163.85182" y="0"> …</t年代pan> <tspan style="font-size: 12.50px; " x="181.42999" y="-1.87"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="311.44" y="-1.87"> (</t年代pan> <tspan style="font-size: 12.50px; " x="315.60349" y="-1.87"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="321.85501" y="-1.87"> b</t年代pan> <tspan style="font-size: 12.50px; " x="328.10651" y="-1.87"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,82.46,-16.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89.78,-13.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.069715" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,133.34,-8.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="9.2200003"> (</t年代pan> <tspan style="font-size: 8.75px; " x="8.9095364" y="9.2200003"> </t年代pan> <tspan style="font-size: 8.75px; " x="13.65312" y="9.2200003"> +</t年代pan> <tspan style="font-size: 8.75px; " x="19.648239" y="9.2200003"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="24.02424" y="9.2200003"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,162.86,-13.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="16.641493" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="35.708569" y="0"> f</t年代pan> <tspan style="font-size: 12.50px; " x="39.484474" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="45.735973" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="54.050468" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="63.765301" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="77.881187" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="82.044685" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="90.609238" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="102.18702" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="107.40077" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="113.65227" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="119.90377" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="127.19302" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="137.44548" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="149.48587" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="155.73737" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="160.93861" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="167.19011" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="172.40387" y="0"> …</t年代pan> <tspan style="font-size: 12.50px; " x="305.70999" y="-1.87"> (</t年代pan> <tspan style="font-size: 12.50px; " x="309.8735" y="-1.87"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="316.125" y="-1.87"> c</t年代pan> <tspan style="font-size: 12.50px; " x="321.67633" y="-1.87"> )</t年代pan> </text> </g> </g> </svg></span><i><span class="displayed-label" id="EEq3.3b"></span><span class="displayed-label" id="EEq3.3c"></span>和<年代vg height="17.8375" id="M42" style="vertical-align:-3.25793pt;width:194.075px;" version="1.1" viewbox="0 0 194.075 17.8375" width="194.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8375)"> <g transform="translate(72,-57.73)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.32,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-24.45,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,8.7,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,19.57,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,37.85,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,48.72,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.231773" y="0"> 1</t年代pan> </text> </g> </g> </svg>。</我></年代pan></p> <p><span class="statement" id="lem2"><span class="statement-title">引理2。</年代pan><i>的最大下界的真正部分本金值是1。</我></年代pan></p> <p>此外,一个具有以下更直观的引理。</p> <p><span class="statement" id="lem3"><span class="statement-title">引理3。</年代pan><i>对于任何给定的<年代vg height="10.8875" id="M43" style="vertical-align:-0.33858pt;width:38.125px;" version="1.1" viewbox="0 0 38.125 10.8875" width="38.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> z</t年代pan> <tspan style="font-size: 12.50px; " x="9.0146627" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.055052" y="0"> ℝ</t年代pan> </text> </g> </g> </svg>,真正的的一部分<年代vg height="14.925" id="M44" style="vertical-align:-3.25793pt;width:41.275002px;" version="1.1" viewbox="0 0 41.275002 14.925" width="41.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> </text> </g> </g> </svg>是不少于<年代vg height="14.8875" id="M45" style="vertical-align:-3.2316pt;width:41.737499px;" version="1.1" viewbox="0 0 41.737499 14.8875" width="41.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.23,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> </text> </g> </g> </svg>对所有<年代vg height="13.125" id="M46" style="vertical-align:-1.95624pt;width:32.325001px;" version="1.1" viewbox="0 0 32.325001 13.125" width="32.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.8521242" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="19.504681" y="0"> 0</t年代pan> </text> </g> </g> </svg>。</我></年代pan></p> <p><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</我></年代pan>考虑三种情况:<年代vg height="16.5375" id="M47" style="vertical-align:-2.21957pt;width:100.6625px;" version="1.1" viewbox="0 0 100.6625 16.5375" width="100.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="34.470772" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="46.04855" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="51.262299" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="59.826855" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.31,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>,<年代vg height="16.5375" id="M48" style="vertical-align:-2.21957pt;width:83.300003px;" version="1.1" viewbox="0 0 83.300003 16.5375" width="83.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="34.470772" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.91,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.04,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> )</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.45" id="M49" style="vertical-align:-2.21957pt;width:66.525002px;" version="1.1" viewbox="0 0 66.525002 13.45" width="66.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="37.371468" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="48.949245" y="0"> )</t年代pan> </text> </g> </g> </svg>分开。<年代pan class="statement" id="casee1"><span class="statement-title"><i class="statement-title">例1 (<年代vg height="16.5375" id="M50" style="vertical-align:-2.21957pt;width:100.6625px;" version="1.1" viewbox="0 0 100.6625 16.5375" width="100.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="34.470772" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="46.04855" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="51.262299" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="59.826855" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.31,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>)。</我></年代pan>在这种情况下,所有分支的兰伯特是复值函数。给出任何<年代vg height="10.8875" id="M51" style="vertical-align:-0.33858pt;width:38.987499px;" version="1.1" viewbox="0 0 38.987499 10.8875" width="38.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> ℝ</t年代pan> </text> </g> </g> </svg>和整数<年代vg height="10.7375" id="M52" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,让<年代vg height="14.8875" id="M53" style="vertical-align:-3.2316pt;width:115.075px;" version="1.1" viewbox="0 0 115.075 14.8875" width="115.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.23,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.069715" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.46,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.44,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.941565" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,14.76,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。假设在<年代vg height="11.2125" id="M54" style="vertical-align:-3.25793pt;width:41.200001px;" version="1.1" viewbox="0 0 41.200001 11.2125" width="41.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2125)"> <g transform="translate(72,-63.03)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.96,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.1875" id="M55" style="vertical-align:-3.2316pt;width:41.662498px;" version="1.1" viewbox="0 0 41.662498 11.1875" width="41.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1875)"> <g transform="translate(72,-63.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.96,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和主要分支<我>k</我>th-branch值,分别有相同的实部<年代vg height="14.625" id="M56" style="vertical-align:-3.25793pt;width:76.625px;" version="1.1" viewbox="0 0 76.625 14.625" width="76.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.91,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.47,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> </g> </g> </svg>。因为在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>,<年代vg height="7.375" id="M57" style="vertical-align:-0.17555pt;width:61.462502px;" version="1.1" viewbox="0 0 61.462502 7.375" width="61.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.375)"> <g transform="translate(72,-66.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.790329" y="0"> →</t年代pan> <tspan style="font-size: 12.50px; " x="28.919439" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.483994" y="0"> ∞</t年代pan> </text> </g> </g> </svg>向右分支段<年代vg height="16.5375" id="M58" style="vertical-align:-2.21957pt;width:100.6625px;" version="1.1" viewbox="0 0 100.6625 16.5375" width="100.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="34.470772" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="46.04855" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="51.262299" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="59.826855" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.31,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>如果,证明将被完成<年代vg height="13.7" id="M59" style="vertical-align:-3.25793pt;width:47.75px;" version="1.1" viewbox="0 0 47.75 13.7" width="47.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7)"> <g transform="translate(72,-61.04)"> <text transform="matrix(1,0,0,-1,-71.95,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.71,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.36,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.09,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>总是正确的。现在<年代vg height="17.75" id="M60" style="vertical-align:-3.25793pt;width:358.36249px;" version="1.1" viewbox="0 0 358.36249 17.75" width="358.36249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.71,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.48,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.76,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.16,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.98,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.928102" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="18.479433" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="24.730934" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="33.770603" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,31.04,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,38.7,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,56.29,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,63.25,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,88.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,95.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.117327" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="25.668659" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="31.920158" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="40.947327" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,143.11,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,151.13,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.73,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,176.05,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,201.06,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.31,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>通过<年代vg height="17.950001" id="M61" style="vertical-align:-3.25793pt;width:203.075px;" version="1.1" viewbox="0 0 203.075 17.950001" width="203.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.95)"> <g transform="translate(72,-57.64)"> <text transform="matrix(1,0,0,-1,-71.95,60.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,57.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,60.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="14.565995" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.47,65.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-24.03,63.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.41,65.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.2816639" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.24,60.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,19.27,57.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,24.52,60.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="14.565995" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,44.65,65.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,54.08,63.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,57.97,65.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.2816639" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,72.14,60.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> </g> </g> </svg>,<年代vg height="14.75" id="M62" style="vertical-align:-3.25793pt;width:123.2875px;" version="1.1" viewbox="0 0 123.2875 14.75" width="123.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.98,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.69,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.368347" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.745838" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="46.08606" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,21.34,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>所有整数<年代vg height="11.0625" id="M63" style="vertical-align:-0.30096pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 11.0625" width="35.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代pan> </text> </g> </g> </svg>与一些<年代vg height="14.5875" id="M64" style="vertical-align:-3.2316pt;width:14.5375px;" version="1.1" viewbox="0 0 14.5375 14.5875" width="14.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.66,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。自<年代vg height="14.0625" id="M65" style="vertical-align:-0.30096pt;width:40.762501px;" version="1.1" viewbox="0 0 40.762501 14.0625" width="40.762501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.39,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.73,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.5875" id="M66" style="vertical-align:-3.2316pt;width:92.837502px;" version="1.1" viewbox="0 0 92.837502 14.5875" width="92.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.55,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.69,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-24.45,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="15.178642" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-3.02,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,一个<年代pan class="equation" id="EEq3.4"> <svg height="307.20001" id="M67" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 307.20001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,307.2)"> <g transform="translate(72,173.76)"> <text transform="matrix(1,0,0,-1,87.67,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.7700005" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.62" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="20.171331" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="26.422832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="33.361996" y="0"> </t年代pan> </text> <text 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transform="matrix(1,0,0,-1,324.21,-129.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,121.03,-161.73)"> <tspan style="font-size: 12.50px; " x="35.689999" y="-9.2299995"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="14.803552" y="0"> −</t年代pan> </text> <text transform="matrix(1,0,0,-1,162.97,-155.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 148.38,-158.61 28.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,148.38,-170.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.679003" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.31,-173.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.83,-164.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> c</t年代pan> <tspan style="font-size: 12.50px; " x="11.401332" y="-2.52"> o</t年代pan> <tspan style="font-size: 12.50px; " x="17.652832" y="-2.52"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="24.591997" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.72,-164.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.74,-161.73)"> <tspan style="font-size: 12.50px; " x="17.6" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.530001" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="255.38" y="-107.73"> (</t年代pan> <tspan style="font-size: 12.50px; " x="259.54349" y="-107.73"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="265.79501" y="-107.73"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.7125" id="M68" style="vertical-align:-3.2316pt;width:138.25px;" version="1.1" viewbox="0 0 138.25 14.7125" width="138.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.98,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.219511" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.821335" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="42.035088" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="48.286587" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="52.450085" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.002377" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="73.342598" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="79.594101" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="83.757599" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="91.359421" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.825" id="M69" style="vertical-align:-3.2316pt;width:65.137497px;" version="1.1" viewbox="0 0 65.137497 14.825" width="65.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-46.94,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.22,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>。因此,<年代vg height="13.7" id="M70" style="vertical-align:-3.25793pt;width:47.75px;" version="1.1" viewbox="0 0 47.75 13.7" width="47.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7)"> <g transform="translate(72,-61.04)"> <text transform="matrix(1,0,0,-1,-71.95,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.71,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.36,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.09,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。为<年代vg height="10.8625" id="M71" style="vertical-align:-0.13794pt;width:46.5px;" version="1.1" viewbox="0 0 46.5 10.8625" width="46.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8625)"> <g transform="translate(72,-63.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.8449" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="12.3" id="M72" style="vertical-align:-1.29163pt;width:53.450001px;" version="1.1" viewbox="0 0 53.450001 12.3" width="53.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="25.056011" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="36.396233" y="0"> 2</t年代pan> </text> </g> </g> </svg>,(<一个href=”#EEq3.3a">5</一个>)和(<一个href=”#EEq3.3c">5度</一个>),分别可以应用于延长上述结果。</年代pan><span class="statement" id="casee2"><span class="statement-title"><i class="statement-title">例2 (<年代vg height="16.5375" id="M73" style="vertical-align:-2.21957pt;width:83.300003px;" version="1.1" viewbox="0 0 83.300003 16.5375" width="83.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="34.470772" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.91,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.04,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> )</t年代pan> </text> </g> </g> </svg>)。</我></年代pan>在这种情况下,本金和−1 st-branch都是实值,并从图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>可以看出<年代vg height="14.75" id="M74" style="vertical-align:-3.25793pt;width:77.224998px;" version="1.1" viewbox="0 0 77.224998 14.75" width="77.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="31.007441" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="36.221191" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="42.472691" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M75" style="vertical-align:-3.13504pt;width:102.075px;" version="1.1" viewbox="0 0 102.075 14.6" width="102.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.92,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="36.333717" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.54747" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="50.112022" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="56.363525" y="0"> ]</t年代pan> </text> </g> </g> </svg>。因此<年代vg height="14.625" id="M76" style="vertical-align:-3.25793pt;width:55.912498px;" version="1.1" viewbox="0 0 55.912498 14.625" width="55.912498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.91,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> </g> </g> </svg>。为<年代vg height="14.75" id="M77" style="vertical-align:-3.25793pt;width:163.4375px;" version="1.1" viewbox="0 0 163.4375 14.75" width="163.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="28.531845" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="33.745598" y="0"> ±</t年代pan> <tspan style="font-size: 12.50px; " x="42.31015" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="48.561653" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="53.762901" y="0"> ±</t年代pan> <tspan style="font-size: 12.50px; " x="62.327454" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="68.578957" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="73.792709" y="0"> …</t年代pan> <tspan style="font-size: 12.50px; " x="88.383705" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="97.760956" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,32.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,40.41,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>意味着<年代pan class="equation" id="EEq3.5"> <svg height="123.9625" id="M78" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 123.9625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,123.9625)"> <g transform="translate(72,27.17)"> <text transform="matrix(1,0,0,-1,91.63,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,97.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,101.87,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,108.34,58.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,120.88,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,128.21,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,153.21,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.23,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,178.83,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,186.15,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,209.08,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.32,58.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.36039" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.37,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,247.25,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.81,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,257.49,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,95.1,36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟹</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,123.82,41.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,128.5,39.54)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,134.97,34.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="14.414555" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,155.64,33.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,160.88,36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,184.39,33.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.72,36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.72,33.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,224.74,36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.34,33.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.66,36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,272.59,33.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,277.83,34.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.36039" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,305.88,33.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,310.75,36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,316.32,41.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,321,39.54)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,95.1,12.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟹</t年代pan> <tspan style="font-size: 12.50px; " x="25.931223" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.271442" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,138.63,9.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,143.87,12.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.43,17.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,154.12,15.16)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.97,12.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.7,9.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,185.57,12.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.14,17.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.82,15.16)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,202.03,12.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,224.95,9.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,95.1,-15.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟹</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,123.82,-10.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,128.5,-12.31)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,132.12,-10.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.8,-12.31)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,150.66,-15.12)"> <tspan style="font-size: 12.50px; " x="36.959999" y="-9.2399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> </text> <text transform="matrix(1,0,0,-1,193.87,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 172.46,-11.99 41.81,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,172.46,-23.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.15,-27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,186.1,-23.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.679003" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,209.03,-27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,215.47,-15.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="258.64999" y="-34.41"> (</t年代pan> <tspan style="font-size: 12.50px; " x="262.81351" y="-34.41"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="269.065" y="-34.41"> )</t年代pan> </text> </g> </g> </svg></span>最后一个的比例(<一个href=”#EEq3.5">7</一个>)显然是不少于团结<年代vg height="14.825" id="M79" style="vertical-align:-3.2316pt;width:59.25px;" version="1.1" viewbox="0 0 59.25 14.825" width="59.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.46,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.89,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是如此,<年代vg height="14.75" id="M80" style="vertical-align:-3.25793pt;width:77.224998px;" version="1.1" viewbox="0 0 77.224998 14.75" width="77.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="31.007441" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="36.221191" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="42.472691" y="0"> )</t年代pan> </text> </g> </g> </svg>。</年代pan><span class="statement" id="casee3"><span class="statement-title"><i class="statement-title">例3 (<年代vg height="13.45" id="M81" style="vertical-align:-2.21957pt;width:66.525002px;" version="1.1" viewbox="0 0 66.525002 13.45" width="66.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="37.371468" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="48.949245" y="0"> )</t年代pan> </text> </g> </g> </svg>)。</我></年代pan>在这种情况下,所有的主枝兰伯特是复值函数。再次,假设在<年代vg height="11.2125" id="M82" style="vertical-align:-3.25793pt;width:41.200001px;" version="1.1" viewbox="0 0 41.200001 11.2125" width="41.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2125)"> <g transform="translate(72,-63.03)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.96,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.1875" id="M83" style="vertical-align:-3.2316pt;width:41.662498px;" version="1.1" viewbox="0 0 41.662498 11.1875" width="41.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1875)"> <g transform="translate(72,-63.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.96,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>分别和主要分支<我>k</我>th-branch值具有相同的实部<年代vg height="14.625" id="M84" style="vertical-align:-3.25793pt;width:76.625px;" version="1.1" viewbox="0 0 76.625 14.625" width="76.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.91,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.47,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> </g> </g> </svg>。请注意只有非负<年代vg height="13.425" id="M85" style="vertical-align:-2.29482pt;width:8.4875002px;" version="1.1" viewbox="0 0 8.4875002 13.425" width="8.4875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>在这种情况下需要讨论。因此,<年代vg height="14.7125" id="M86" style="vertical-align:-3.2316pt;width:92.474998px;" version="1.1" viewbox="0 0 92.474998 14.7125" width="92.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.86,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.15,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> )</t年代pan> </text> </g> </g> </svg>,因为这里<年代vg height="14.7125" id="M87" style="vertical-align:-3.2316pt;width:138.25px;" version="1.1" viewbox="0 0 138.25 14.7125" width="138.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.98,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="20.354883" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="26.606384" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.158676" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="47.498898" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="53.750397" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="65.515717" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="70.729469" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="76.980972" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="83.757599" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="91.359421" y="0"> )</t年代pan> </text> </g> </g> </svg>为<年代vg height="11.0625" id="M88" style="vertical-align:-0.30096pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 11.0625" width="35.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.7125" id="M89" style="vertical-align:-3.2316pt;width:138.25px;" version="1.1" viewbox="0 0 138.25 14.7125" width="138.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.98,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.219511" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.821335" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="42.035088" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="46.198586" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="52.450085" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.002377" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="73.342598" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="79.594101" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="83.757599" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="91.359421" y="0"> )</t年代pan> </text> </g> </g> </svg>为<年代vg height="11.0625" id="M90" style="vertical-align:-0.30096pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 11.0625" width="35.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代pan> </text> </g> </g> </svg>,但<年代vg height="14.7125" id="M91" style="vertical-align:-3.2316pt;width:122.65px;" version="1.1" viewbox="0 0 122.65 14.7125" width="122.65" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.69,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-24.45,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.94,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,7.78,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>的范围<年代vg height="11.05" id="M92" style="vertical-align:-3.2316pt;width:14.4875px;" version="1.1" viewbox="0 0 14.4875 11.05" width="14.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>可以是有限的<年代vg height="14.7125" id="M93" style="vertical-align:-3.2316pt;width:150.41251px;" version="1.1" viewbox="0 0 150.41251 14.7125" width="150.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.98,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="20.354883" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="26.606384" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.158676" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="47.498898" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="53.750397" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="57.226231" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="63.47773" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="67.641228" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="75.243057" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="80.456802" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="86.708305" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="93.484932" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="101.08675" y="0"> )</t年代pan> </text> </g> </g> </svg>为<年代vg height="11.0625" id="M94" style="vertical-align:-0.30096pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 11.0625" width="35.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.7125" id="M95" style="vertical-align:-3.2316pt;width:150.41251px;" version="1.1" viewbox="0 0 150.41251 14.7125" width="150.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.98,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.219511" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.821335" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="42.035088" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="46.198586" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="52.450085" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.002377" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="73.342598" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="79.594101" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="83.069931" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="89.321434" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="93.484932" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="101.08675" y="0"> )</t年代pan> </text> </g> </g> </svg>为<年代vg height="11.0625" id="M96" style="vertical-align:-0.30096pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 11.0625" width="35.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代pan> </text> </g> </g> </svg>。因为在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个><年代vg height="7.375" id="M97" style="vertical-align:-0.17555pt;width:53.362499px;" version="1.1" viewbox="0 0 53.362499 7.375" width="53.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.375)"> <g transform="translate(72,-66.1)"> <text transform="matrix(1,0,0,-1,-69.87,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.790329" y="0"> →</t年代pan> <tspan style="font-size: 12.50px; " x="28.931942" y="0"> ∞</t年代pan> </text> </g> </g> </svg>向右分支段<年代vg height="13.45" id="M98" style="vertical-align:-2.21957pt;width:66.525002px;" version="1.1" viewbox="0 0 66.525002 13.45" width="66.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="25.906216" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="37.371468" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="48.949245" y="0"> )</t年代pan> </text> </g> </g> </svg>如果,证明将被完成<年代vg height="13.7" id="M99" style="vertical-align:-3.25793pt;width:47.75px;" version="1.1" viewbox="0 0 47.75 13.7" width="47.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7)"> <g transform="translate(72,-61.04)"> <text transform="matrix(1,0,0,-1,-71.95,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.71,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.36,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.09,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>总是正确的。现在<年代vg height="17.75" id="M100" style="vertical-align:-3.25793pt;width:252.5px;" version="1.1" viewbox="0 0 252.5 17.75" width="252.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.71,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.69,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.11,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.76,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.16,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.98,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.928102" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="18.479433" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="24.730934" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="33.770603" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,31.04,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,39.06,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,56.66,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,63.98,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,88.99,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,94.24,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="6.926662" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.968491" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,124.77,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代pan class="equation" id="EEq3.6"> <svg height="90.287498" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 90.287498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,90.2875)"> <g transform="translate(72,0.23)"> <text transform="matrix(1,0,0,-1,79.96,51.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.7771063" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="14.328438" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="20.579939" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.519102" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,113.74,48.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,121.76,51.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,139.35,48.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,146.68,51.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.61,48.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,177.63,51.8)"> <tspan style="font-size: 12.50px; " x="42.310001" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.492657" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="33.533047" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="51.689999" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="57.241333" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="63.492832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="70.431999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.32,48.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.34,51.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-9.2299995"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="17.403667" y="-9.2299995"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="20.879501" y="-9.2299995"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,289.47,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,294.35,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,300.6,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 274.88,54.92 30.96,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,275.24,43.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,300.24,39.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,309.81,51.8)"> <tspan style="font-size: 12.50px; " x="17.6" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-89.870003" y="47.049999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-67.300003" y="32.48"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-110.68" y="39.73"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-98.652115" y="39.73"> </t年代pan> </text> <g> <path d="m 230.52,15.2 30.24,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,230.52,3.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,255.52,0.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,264.73,12.07)"> <tspan style="font-size: 12.50px; " x="17.6" y="7.3200002"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.059999" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="209.39" y="-20.690001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="213.5535" y="-20.690001"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="219.80499" y="-20.690001"> )</t年代pan> </text> </g> </g> </svg></span>因此,完成证明。</年代pan></span></p> <h4 id="the-spectrum-of-first-order-feedback-time-delay-systems">4所示。的光谱一阶时滞系统的反馈</h4><p>考虑一阶时滞系统(<一个href=”#EEq2.2">2</一个>)。让<年代vg height="10.8125" id="M102" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>的特征值(<一个href=”#EEq2.2">2</一个>)。然后[<一个href=”#B9">9</一个>]<年代pan class="equation" id="EEq4.1"> <svg height="121.75" id="M103" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 121.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,121.75)"> <g transform="translate(72,25.4)"> <text transform="matrix(1,0,0,-1,120.16,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.880011" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,147.32,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,154.97,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,172.59,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,177.47,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,183.03,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.729952" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,202.78,60.97)"> <tspan style="font-size: 12.50px; " x="-46.700001" y="26.209999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-79.150002" y="23.700001"> ⟺</t年代pan> <tspan style="font-size: 12.50px; " x="-56.006947" y="23.700001"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="-40.849998" y="23.700001"> </t年代pan> <tspan style="font-size: 12.50px; " x="-31.310211" y="23.700001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="-19.96999" y="23.700001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,189.1,34.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,193.97,34.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.47,42.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 8.75px; " x="5.0499039" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="7.9643202" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="12.699152" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="18.694271" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.56,40.09)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,234.18,42.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,241.07,37.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,259.38,34.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,264.25,37.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,277.03,42.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,287.42,40.09)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,291.05,42.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,123.63,12.77)"> <tspan style="font-size: 12.50px; " x="38.720001" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.57" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟺</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.47,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,179.35,12.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.13,17.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,202.51,15.58)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.14,17.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.69,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.66" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.52"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.347885" y="-2.52"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="36.509998" y="-2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.049789" y="-2.52"> −</t年代pan> <tspan style="font-size: 12.50px; " x="57.390011" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,275.36,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.24,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="-109.5" y="19.469999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-156.61" y="26.719999"> ⟺</t年代pan> <tspan style="font-size: 12.50px; " x="-133.46695" y="26.719999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-123.22699" y="26.719999"> =</t年代pan> </text> <g> <path d="m 170.25,-13.34 7.22,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,170.25,-25.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.98" y="-6.2399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.83" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.35,-19.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.23,-16.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,224.01,-11.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,234.4,-13.65)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,238.02,-11.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,243.57,-18.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="19.957718" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.82,-19.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,274.69,-16.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="199.42999" y="-36.650002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="203.59351" y="-36.650002"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="209.845" y="-36.650002"> )</t年代pan> </text> </g> </g> </svg></span>根据朗伯函数,<年代vg height="17.9125" id="M104" style="vertical-align:-3.25793pt;width:166.72501px;" version="1.1" viewbox="0 0 166.72501 17.9125" width="166.72501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.52,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.87,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.05,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.18,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,9.26,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,14.14,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,26.92,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,37.31,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,40.93,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,46.48,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>被称为主要特征值,<年代vg height="17.9125" id="M105" style="vertical-align:-3.25793pt;width:167.64999px;" version="1.1" viewbox="0 0 167.64999 17.9125" width="167.64999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.47,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.16,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.5,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.68,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.44,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,10,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,14.87,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,27.65,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,38.04,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,41.66,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,47.21,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>,<年代vg height="12.8875" id="M106" style="vertical-align:-1.76814pt;width:101.4875px;" version="1.1" viewbox="0 0 101.4875 12.8875" width="101.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-67.78,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> ±</t年代pan> <tspan style="font-size: 12.50px; " x="30.8449" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.096401" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="42.31015" y="0"> ±</t年代pan> <tspan style="font-size: 12.50px; " x="50.874706" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="57.126205" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="62.327454" y="0"> …</t年代pan> </text> </g> </g> </svg>,被称为<我>k</我>th-branch特征值。注意,参数<年代vg height="11.075" id="M107" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.925" id="M108" style="vertical-align:-3.13504pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 10.925" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.95" id="M109" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>一阶系统的都是真实的,所以只有<我><我>β</我></我>讨论了= 0 (<一个href=”#EEq3.1">3</一个>)。通过上面的结果有一些属性的特征值(<一个href=”#EEq2.2">2</一个>),可以立即获得。<年代pan class="list"><span class="list-item"><span class="list-label">(我)</年代pan><span class="list-content"> <svg height="14.75" id="M110" style="vertical-align:-3.25793pt;width:219.85001px;" version="1.1" viewbox="0 0 219.85001 14.75" width="219.85001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-45.05,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="37.72155" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="41.885052" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,8.49,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> k</t年代pan> </text> <text transform="matrix(1,0,0,-1,13.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="35.821095" y="0"> ±</t年代pan> <tspan style="font-size: 12.50px; " x="44.385651" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="50.63715" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="55.850903" y="0"> ±</t年代pan> <tspan style="font-size: 12.50px; " x="64.415459" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="70.666954" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="75.880707" y="0"> …</t年代pan> </text> </g> </g> </svg>对于任意给定的一组<年代vg height="11.075" id="M111" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.925" id="M112" style="vertical-align:-3.13504pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 10.925" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="10.95" id="M113" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。</年代pan></span><span class="list-item"><span class="list-label">(2)</年代pan><span class="list-content"><span class="equation" id="eq1"> <svg height="90.087502" id="M114" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 90.087502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,90.0875)"> <g transform="translate(72,0.07)"> <text transform="matrix(1,0,0,-1,134.3,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,140.57,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,145.45,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,158.23,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.62,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,172.24,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,181.26,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.43,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,221.77,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟺</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.69,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,260.03,60.97)"> <tspan style="font-size: 12.50px; " x="-142.78" y="28.42"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> ℝ</t年代pan> <tspan style="font-size: 12.50px; " x="21.380131" y="0"> ,</t年代pan> </text> <text transform="matrix(1,0,0,-1,123.52,29.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,128.4,32.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,141.18,37.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,151.56,35.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,155.19,37.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,164.21,32.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,190.38,37.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,204.72,32.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟺</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,234.64,29.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,242.98,32.55)"> <tspan style="font-size: 12.50px; " x="22.280001" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> </text> <g> <path d="m 264.78,35.68 7.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,264.78,23.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="11.19" y="-8.75"> +</t年代pan> <tspan style="font-size: 12.50px; " x="22.530222" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,293.59,29.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,298.46,32.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-163.89999" y="28.82"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,140.84,0.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,145.71,3.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,158.49,8.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.88,6.54)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,172.5,8.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,181.52,3.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.69,8.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,222.03,3.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟺</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.95,0.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,260.3,3.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> ℂ</t年代pan> <tspan style="font-size: 12.50px; " x="20.842501" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="207.57001" y="-29.110001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="211.73351" y="-29.110001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="217.985" y="-29.110001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="224.2365" y="-29.110001"> )</t年代pan> </text> </g> </g> </svg></span></span></span><span class="list-item"><span class="list-label">(3)</年代pan><span class="list-content"> <svg height="14.8625" id="M115" style="vertical-align:-3.25793pt;width:207.9375px;" version="1.1" viewbox="0 0 207.9375 14.8625" width="207.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="14.816055" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="28.281786" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="39.622005" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.05,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-17.7,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="14.115887" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="22.455387" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="30.094721" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="34.258221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,23.33,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,28.2,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,56.65,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,61.53,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.263763" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="16.616488" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="19.117086" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,86.92,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,91.8,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> </g> </g> </svg>。</年代pan></span><span class="list-item"><span class="list-label">(iv)</年代pan><span class="list-content"> <svg height="14.8625" id="M116" style="vertical-align:-3.25793pt;width:119.7125px;" version="1.1" viewbox="0 0 119.7125 14.8625" width="119.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="28.00672" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="41.897552" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="46.06105" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-19.12,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.24,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.269043" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="30.744877" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。</年代pan></span></span></p> <p>这些属性是立即节中所暗示的结果<一个href=”#sec3">3</一个>。上界的财产(iii),让<年代vg height="13.4875" id="M117" style="vertical-align:-2.34499pt;width:71.512497px;" version="1.1" viewbox="0 0 71.512497 13.4875" width="71.512497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.382771" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="43.722992" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.586658" y="0"> </t年代pan> </text> </g> </g> </svg>,从<年代vg height="17.9125" id="M118" style="vertical-align:-3.25793pt;width:100.8px;" version="1.1" viewbox="0 0 100.8 17.9125" width="100.8" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.4,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.75,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.13,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-13.25,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-7.69,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.729952" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>一个人<年代vg height="17.9125" id="M119" style="vertical-align:-3.25793pt;width:171.45px;" version="1.1" viewbox="0 0 171.45 17.9125" width="171.45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.802592" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.842981" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.82,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.17,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-17.55,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-12.68,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-7.11,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="11.123792" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,11.65,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.558052" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="42.072594" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="49.286827" y="0"> )</t年代pan> </text> </g> </g> </svg>。因此,<年代pan class="equation" id="eq2"> <svg height="18.7875" id="M120" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.7875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7875)"> <g transform="translate(72,-56.97)"> <text transform="matrix(1,0,0,-1,85.57,60.98)"> <tspan style="font-size: 12.50px; " x="27.85" y="-1.74"> |</t年代pan> <tspan style="font-size: 12.50px; " x="27.85" y="1.74"> |</t年代pan> <tspan style="font-size: 12.50px; " x="30.35" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.8273582" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.803792" y="0"> =</t年代pan> </text> <text transform="matrix(1,0,0,-1,122.19,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,129.85,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,147.47,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,152.34,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,157.91,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="11.123792" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.67,60.97)"> <tspan style="font-size: 12.50px; " x="53.450001" y="-1.75"> |</t年代pan> <tspan style="font-size: 12.50px; " x="53.450001" y="1.73"> |</t年代pan> <tspan style="font-size: 12.50px; " x="59.43" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="73.550003" y="-1.59"> |</t年代pan> <tspan style="font-size: 12.50px; " x="73.550003" y="1.5700001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="76.050003" y="-7.1054274e-015"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.558052" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="42.072594" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="49.286827" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,259,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,263.87,62.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.2800002" y="1.59"> +</t年代pan> <tspan style="font-size: 12.50px; " x="16.620001" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="16.620001" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="19.120001" y="1.59"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.27,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,294.15,62.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="4.5799999" y="-0.16"> |</t年代pan> <tspan style="font-size: 12.50px; " x="4.5799999" y="3.3199999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="7.0799999" y="1.59"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.79,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="11.132544" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,323.47,62.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.48"> |</t年代pan> <tspan style="font-size: 12.50px; " x="4.5900002" y="1.75"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="144.39999" y="1.75"> (</t年代pan> <tspan style="font-size: 12.50px; " x="148.56349" y="1.75"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="154.815" y="1.75"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="161.0665" y="1.75"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>如果<年代vg height="11.0625" id="M121" style="vertical-align:-0.30096pt;width:36.5px;" version="1.1" viewbox="0 0 36.5 11.0625" width="36.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.802592" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.842981" y="0"> 0</t年代pan> </text> </g> </g> </svg>然后<年代vg height="14.75" id="M122" style="vertical-align:-3.25793pt;width:122.475px;" version="1.1" viewbox="0 0 122.475 14.75" width="122.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-45.05,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-11.72,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.2762661" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="16.616488" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="19.117086" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,18.55,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,23.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> </g> </g> </svg>,如果<年代vg height="12.3" id="M123" style="vertical-align:-1.29163pt;width:36.5px;" version="1.1" viewbox="0 0 36.5 12.3" width="36.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.802592" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="22.842981" y="0"> 0</t年代pan> </text> </g> </g> </svg>然后<年代vg height="14.75" id="M124" style="vertical-align:-3.25793pt;width:72.25px;" version="1.1" viewbox="0 0 72.25 14.75" width="72.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-45.05,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代pan> </text> </g> </g> </svg>。</p> <h4 id="applications-to-some-control-issues">5。应用程序控制问题</h4><p>不失一般性,随后让<我>b</我>是一个给定的积极的常数。</p> <h5 id="sec5.1">5.1。状态反馈对系统稳定</h5><p>对于系统(<一个href=”#EEq2.1">1</一个>与状态反馈)<年代vg height="13.45" id="M125" style="vertical-align:-2.21957pt;width:78.025002px;" version="1.1" viewbox="0 0 78.025002 13.45" width="78.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.00336" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="21.63019" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="33.670578" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.197865" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.074516" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="54.238014" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="58.151451" y="0"> )</t年代pan> </text> </g> </g> </svg>、财产(ii)的部分<一个href=”#sec4">4</一个>显示的主要特征值(<一个href=”#EEq2.2">2</一个>)是实值为<年代vg height="16.612499" id="M126" style="vertical-align:-2.21957pt;width:132.1375px;" version="1.1" viewbox="0 0 132.1375 16.612499" width="132.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="27.806671" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="39.146893" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.23,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.36,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,9.94,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,20.33,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,23.95,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,29.5,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>和复数<年代vg height="16.612499" id="M127" style="vertical-align:-2.21957pt;width:125.1875px;" version="1.1" viewbox="0 0 125.1875 16.612499" width="125.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.78,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.91,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,4.38,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,14.77,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,18.39,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,23.94,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>。此外,房地产(i)的部分<一个href=”#sec4">4</一个>校长最大特征值的实部在所有特征值。稳定系统(<一个href=”#EEq2.2">2</一个>),一个主要的特征值转移到左边半平面(LHP)。</p> <p><span class="statement" id="thm1"><span class="statement-title">定理4。</年代pan><i>存在一个状态反馈增益K,这样系统(<一个href=”#EEq2.2">2</一个>)可以渐近稳定当且仅当<年代vg height="14.8625" id="M128" style="vertical-align:-3.25793pt;width:54.625px;" version="1.1" viewbox="0 0 54.625 14.8625" width="54.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.767723" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。</我></年代pan></p> <p><span class="statement" id="proof2"><span class="statement-title"><i class="statement-title">证明。</我></年代pan>假设<年代vg height="14.8625" id="M129" style="vertical-align:-3.25793pt;width:54.625px;" version="1.1" viewbox="0 0 54.625 14.8625" width="54.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.767723" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。然后属性(iii)的部分<一个href=”#sec4">4</一个>显示,<年代vg height="14.75" id="M130" style="vertical-align:-3.25793pt;width:74.862503px;" version="1.1" viewbox="0 0 74.862503 14.75" width="74.862503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="32.18272" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="39.809551" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="43.973049" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.2,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>不管什么<年代vg height="10.325" id="M131" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是多少。另一方面,如果<年代vg height="14.8625" id="M132" style="vertical-align:-3.25793pt;width:54.625px;" version="1.1" viewbox="0 0 54.625 14.8625" width="54.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.767723" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>,或<年代vg height="14.8625" id="M133" style="vertical-align:-3.25793pt;width:75.5px;" version="1.1" viewbox="0 0 75.5 14.8625" width="75.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.8,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="9.9898968" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.330118" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="42.897793" y="0"> 1</t年代pan> </text> </g> </g> </svg>对于一些<年代vg height="11.0625" id="M134" style="vertical-align:-0.30096pt;width:34.887501px;" version="1.1" viewbox="0 0 34.887501 11.0625" width="34.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5147829" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="21.555172" y="0"> 0</t年代pan> </text> </g> </g> </svg>,然后在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>可以看出,有一个<年代vg height="10.325" id="M135" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>这样<年代vg height="17.9125" id="M136" style="vertical-align:-3.25793pt;width:206.35001px;" version="1.1" viewbox="0 0 206.35001 17.9125" width="206.35001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.690785" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.567196" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="26.781425" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.25,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-10.86,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-7.24,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.69,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.231773" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.258942" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="48.599159" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.650612" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="58.126446" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="67.853783" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="79.894173" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="88.458725" y="0"> 1</t年代pan> </text> </g> </g> </svg>,这使得<年代vg height="14.8625" id="M137" style="vertical-align:-3.25793pt;width:111.125px;" version="1.1" viewbox="0 0 111.125 14.8625" width="111.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.643892" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="30.119726" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="34.283226" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="40.534725" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="55.38829" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="67.42868" y="0"> 0</t年代pan> </text> </g> </g> </svg>。</年代pan></p> <p><span class="statement" id="thm2"><span class="statement-title">定理5。</年代pan><i>假设<年代vg height="14.8625" id="M138" style="vertical-align:-3.25793pt;width:54.625px;" version="1.1" viewbox="0 0 54.625 14.8625" width="54.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.767723" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>在(<一个href=”#EEq2.1">1</一个>)。K的渐近稳定的范围(<一个href=”#EEq2.1">1</一个>)是<年代vg height="14.8625" id="M139" style="vertical-align:-3.25793pt;width:149.075px;" version="1.1" viewbox="0 0 149.075 14.8625" width="149.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.97,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.1,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.27,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.6,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="17.929302" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,28.82,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,33.69,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3522444" y="0"> )</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="14.8625" id="M140" style="vertical-align:-3.25793pt;width:91.862503px;" version="1.1" viewbox="0 0 91.862503 14.8625" width="91.862503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.8,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.82,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.715311" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-3.43,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M141" style="vertical-align:-3.25793pt;width:67.662498px;" version="1.1" viewbox="0 0 67.662498 14.75" width="67.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.35,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.258461" y="0"> )</t年代pan> </text> </g> </g> </svg>。</我></年代pan></p> <p><span class="statement" id="proof3"><span class="statement-title"><i class="statement-title">证明。</我></年代pan>的值<年代vg height="10.325" id="M142" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>(渐近稳定的<一个href=”#EEq2.1">1</一个>这些呈现的实部)<年代vg height="17.9125" id="M143" style="vertical-align:-3.25793pt;width:172.03751px;" version="1.1" viewbox="0 0 172.03751 17.9125" width="172.03751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.52,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.87,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.05,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.18,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.690785" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.567196" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="26.781425" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,31.17,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,41.56,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,45.18,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,50.73,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>小于0,或者<年代vg height="17.9125" id="M144" style="vertical-align:-3.25793pt;width:93.150002px;" version="1.1" viewbox="0 0 93.150002 17.9125" width="93.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.690785" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.567196" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="26.781425" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.25,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-10.86,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-7.24,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.69,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>小于<年代vg height="14.8625" id="M145" style="vertical-align:-3.25793pt;width:33.787498px;" version="1.1" viewbox="0 0 33.787498 14.8625" width="33.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.11,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.23,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。从图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>的假设<年代vg height="14.8625" id="M146" style="vertical-align:-3.25793pt;width:54.625px;" version="1.1" viewbox="0 0 54.625 14.8625" width="54.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.767723" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>或<年代vg height="14.8625" id="M147" style="vertical-align:-3.25793pt;width:71.699997px;" version="1.1" viewbox="0 0 71.699997 14.8625" width="71.699997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="30.319775" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="38.884331" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.78,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.91,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>,一个非空范围的稳定收益<年代vg height="10.325" id="M148" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>存在,稳定收益<年代vg height="10.325" id="M149" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>必须躺在的范围<年代vg height="14.6" id="M150" style="vertical-align:-3.13504pt;width:53.049999px;" version="1.1" viewbox="0 0 53.049999 14.6" width="53.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.39,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.65,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.77,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="14.2375" id="M151" style="vertical-align:-3.13504pt;width:18.125px;" version="1.1" viewbox="0 0 18.125 14.2375" width="18.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.42,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>使<年代vg height="14.8625" id="M152" style="vertical-align:-3.25793pt;width:67.625px;" version="1.1" viewbox="0 0 67.625 14.8625" width="67.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.91,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.03,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.16,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>与<年代pan class="equation" id="EEq5.1"> <svg height="18.5375" id="M153" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5375)"> <g transform="translate(72,-57.17)"> <text transform="matrix(1,0,0,-1,161.35,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,170.87,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.75,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.87641" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="13.090641" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.4,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,204.79,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,208.41,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,217.44,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.16,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,241.04,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,246.6,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.28,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,467.87,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> )</t年代pan> </text> </g> </g> </svg></span>和<年代vg height="14.2375" id="M154" style="vertical-align:-3.13504pt;width:18.125px;" version="1.1" viewbox="0 0 18.125 14.2375" width="18.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.42,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>使<年代vg height="14.8625" id="M155" style="vertical-align:-3.25793pt;width:147.1125px;" version="1.1" viewbox="0 0 147.1125 14.8625" width="147.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.91,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.03,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.16,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="31.282507" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,12.38,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,17.25,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.715311" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.266644" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,40.77,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>与<年代vg height="14.75" id="M156" style="vertical-align:-3.25793pt;width:67.662498px;" version="1.1" viewbox="0 0 67.662498 14.75" width="67.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.35,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.258461" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代pan class="equation" id="EEq5.2"> <svg height="101.375" id="M157" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 101.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,101.375)"> <g transform="translate(72,9.1)"> <text transform="matrix(1,0,0,-1,92.65,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,102.18,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,107.05,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.87641" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="13.090641" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,125.71,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,136.09,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,139.72,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,148.74,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,166.34,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.02,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,177.23,58.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,189.77,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,196.73,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.73,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.38,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,246.98,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,253.93,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.679003" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,276.86,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,281.74,58.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="-133" y="21.870001"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-120.97211" y="21.870001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="-112.40756" y="21.870001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.91,41.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.59,39.41)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,185.79,34.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,197.9,33.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,202.77,36.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.715311" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.28,33.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,233.24,36.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.24,33.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,265.9,36.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,283.49,33.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,290.45,36.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,313.38,33.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,318.25,34.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="-146.56" y="21.860001"> </t年代pan> <tspan style="font-size: 12.50px; " x="-169.50999" y="31.129999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-157.48212" y="31.129999"> −</t年代pan> </text> <text transform="matrix(1,0,0,-1,177.25,17.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,181.94,15.03)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,186.06,12.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.31,9.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <g> <path d="m 170.54,6.08 27.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,170.54,-5.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,193.46,-8.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,199.53,2.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="268.34" y="-25.379999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="272.50351" y="-25.379999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="278.755" y="-25.379999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="285.0065" y="-25.379999"> )</t年代pan> </text> </g> </g> </svg></span>因此,<年代vg height="14.8625" id="M158" style="vertical-align:-3.25793pt;width:133.2px;" version="1.1" viewbox="0 0 133.2 14.8625" width="133.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.42,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.08,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.22,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.35,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,25.48,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,30.35,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M159" style="vertical-align:-3.25793pt;width:73.849998px;" version="1.1" viewbox="0 0 73.849998 14.75" width="73.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.42,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.08,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.2,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.32,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> </g> </g> </svg>。</年代pan></p> <p>定理的结果<一个href=”#thm2">5</一个>在[<一个href=”#B18">18</一个>),但提供了一个不同的推导。</p> <p><span class="statement" id="deff1"><span class="statement-title"><i class="statement-title">定义6。</我></年代pan>对于一个给定的<年代vg height="11.175" id="M160" style="vertical-align:-0.30096pt;width:36.349998px;" version="1.1" viewbox="0 0 36.349998 11.175" width="36.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.175)"> <g transform="translate(72,-63.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> 0</t年代pan> </text> </g> </g> </svg>的范围,稳定收益<我>K</我>表示为<年代vg height="14.7125" id="M161" style="vertical-align:-3.22282pt;width:18.3375px;" version="1.1" viewbox="0 0 18.3375 14.7125" width="18.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。</年代pan></p> <h5 id="sec5.2">5.2。鲁棒稳定性对延迟的大小</h5><p>的延迟时间<年代vg height="10.95" id="M162" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>在(<一个href=”#EEq2.1">1</一个>)被认为是一个常数,但可能是不确定的。在实际应用中,延迟时间<年代vg height="10.95" id="M163" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>可能无法准确估计。因此,重要的是要分析健壮的系统(<一个href=”#EEq2.2">2</一个>)是关于延迟时间<年代vg height="10.95" id="M164" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>在选定的稳定状态反馈增益<年代vg height="13.125" id="M165" style="vertical-align:-1.95624pt;width:37.012501px;" version="1.1" viewbox="0 0 37.012501 13.125" width="37.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="23.255581" y="0"> 0</t年代pan> </text> </g> </g> </svg>。基于的迹象<年代vg height="11.075" id="M166" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="10.325" id="M167" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>4例分别进行了讨论。</p> <p><span class="statement" id="casee10"><span class="statement-title"><i class="statement-title">例1 (<年代vg height="14.75" id="M168" style="vertical-align:-3.25793pt;width:41.262501px;" version="1.1" viewbox="0 0 41.262501 14.75" width="41.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.0625" id="M169" style="vertical-align:-0.30096pt;width:39.237499px;" version="1.1" viewbox="0 0 39.237499 11.0625" width="39.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> 0</t年代pan> </text> </g> </g> </svg>)。</我></年代pan>自<年代vg height="10.95" id="M170" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>是一个积极的延迟时间,定理的条件吗<一个href=”#thm1">4</一个>适用于所有<年代vg height="14.75" id="M171" style="vertical-align:-3.25793pt;width:41.262501px;" version="1.1" viewbox="0 0 41.262501 14.75" width="41.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>。选择一个积极的<年代vg height="14.7125" id="M172" style="vertical-align:-3.22282pt;width:54.349998px;" version="1.1" viewbox="0 0 54.349998 14.7125" width="54.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.83,64.01)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="12" id="M173" style="vertical-align:-0.1254pt;width:15.4875px;" version="1.1" viewbox="0 0 15.4875 12" width="15.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12)"> <g transform="translate(72,-62.4)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.74,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>是假定的延迟的大小。因此<年代vg height="14.75" id="M174" style="vertical-align:-3.25793pt;width:74.699997px;" version="1.1" viewbox="0 0 74.699997 14.75" width="74.699997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="27.806671" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="39.146893" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.64,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> </g> </g> </svg>上限是独立的<年代vg height="10.95" id="M175" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg><i>。</我>而且,通过定理<一个href=”#thm2">5</一个>的下界<年代vg height="14.7125" id="M176" style="vertical-align:-3.22282pt;width:18.3375px;" version="1.1" viewbox="0 0 18.3375 14.7125" width="18.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>负的所有<年代vg height="11.175" id="M177" style="vertical-align:-0.30096pt;width:36.349998px;" version="1.1" viewbox="0 0 36.349998 11.175" width="36.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.175)"> <g transform="translate(72,-63.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> 0</t年代pan> </text> </g> </g> </svg>。因此,积极<年代vg height="10.325" id="M178" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是在<年代vg height="14.7125" id="M179" style="vertical-align:-3.22282pt;width:18.3375px;" version="1.1" viewbox="0 0 18.3375 14.7125" width="18.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>对所有<年代vg height="11.175" id="M180" style="vertical-align:-0.30096pt;width:36.349998px;" version="1.1" viewbox="0 0 36.349998 11.175" width="36.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.175)"> <g transform="translate(72,-63.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> 0</t年代pan> </text> </g> </g> </svg>。简而言之,反馈系统是渐近稳定独立的延迟时间<我>h</我>。</年代pan></p> <p><span class="statement" id="casee20"><span class="statement-title"><i class="statement-title">例2 (<年代vg height="14.75" id="M181" style="vertical-align:-3.25793pt;width:41.262501px;" version="1.1" viewbox="0 0 41.262501 14.75" width="41.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.0625" id="M182" style="vertical-align:-0.30096pt;width:39.237499px;" version="1.1" viewbox="0 0 39.237499 11.0625" width="39.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> 0</t年代pan> </text> </g> </g> </svg>)。</我></年代pan>假设一个负<年代vg height="14.7125" id="M183" style="vertical-align:-3.22282pt;width:54.349998px;" version="1.1" viewbox="0 0 54.349998 14.7125" width="54.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.83,64.01)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>被选中,<年代vg height="12" id="M184" style="vertical-align:-0.1254pt;width:15.4875px;" version="1.1" viewbox="0 0 15.4875 12" width="15.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12)"> <g transform="translate(72,-62.4)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.74,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>是假定的延迟的大小。请注意,主特征值<年代vg height="17.9125" id="M185" style="vertical-align:-3.25793pt;width:172.03751px;" version="1.1" viewbox="0 0 172.03751 17.9125" width="172.03751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.52,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.87,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.05,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.18,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.690785" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.567196" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="26.781425" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,31.17,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,41.56,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,45.18,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,50.73,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>,所以如果<年代vg height="12.225" id="M186" style="vertical-align:-0.30096pt;width:43.887501px;" version="1.1" viewbox="0 0 43.887501 12.225" width="43.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.225)"> <g transform="translate(72,-62.22)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.01,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>然后<年代vg height="14.025" id="M187" style="vertical-align:-0.13794pt;width:59.787498px;" version="1.1" viewbox="0 0 59.787498 14.025" width="59.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.025)"> <g transform="translate(72,-60.78)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5272856" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.617928" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.78,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.39,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.77,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>更少的负面,通过观察的主要分支图的参数值吗<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>,它可以推断<年代vg height="14.625" id="M188" style="vertical-align:-3.25793pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.625" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>将留在LHP。然而,当<年代vg height="12" id="M189" style="vertical-align:-0.1254pt;width:42.162498px;" version="1.1" viewbox="0 0 42.162498 12" width="42.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12)"> <g transform="translate(72,-62.4)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="9.9898968" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.330118" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.4,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>足够大,真正的一部分吗<年代vg height="17.9125" id="M190" style="vertical-align:-3.25793pt;width:93.150002px;" version="1.1" viewbox="0 0 93.150002 17.9125" width="93.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.47,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.6,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.690785" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.567196" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="26.781425" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.25,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-10.86,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-7.24,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.69,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>会变得积极。更具体地说,在定理的证明<一个href=”#thm2">5</一个>,如果<年代vg height="14.8625" id="M191" style="vertical-align:-3.25793pt;width:91.862503px;" version="1.1" viewbox="0 0 91.862503 14.8625" width="91.862503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.8,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.82,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.715311" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-3.43,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>与一些<年代vg height="14.75" id="M192" style="vertical-align:-3.25793pt;width:81.5px;" version="1.1" viewbox="0 0 81.5 14.75" width="81.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.35,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.793209" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="27.269043" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="33.520542" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="38.734295" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.336117" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.8625" id="M193" style="vertical-align:-3.25793pt;width:235.8px;" version="1.1" viewbox="0 0 235.8 14.8625" width="235.8" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.1,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.22,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="41.559971" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,20.6,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,25.48,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.231773" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,59.99,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,64.87,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.591241" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="21.142572" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="27.394073" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="36.421238" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,107.55,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,112.43,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>,然后<年代vg height="14.625" id="M194" style="vertical-align:-3.25793pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.625" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>将搬到LHP的边界。请注意,这样的<年代vg height="11.075" id="M195" style="vertical-align:-3.25793pt;width:14.0375px;" version="1.1" viewbox="0 0 14.0375 11.075" width="14.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>当且仅当存在<年代vg height="14.75" id="M196" style="vertical-align:-3.25793pt;width:57.049999px;" version="1.1" viewbox="0 0 57.049999 14.75" width="57.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.64,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.76,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> </g> </g> </svg>,这意味着如果<年代vg height="14.75" id="M197" style="vertical-align:-3.25793pt;width:57.049999px;" version="1.1" viewbox="0 0 57.049999 14.75" width="57.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.64,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.76,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> </g> </g> </svg>反馈系统是独立于稳定<年代vg height="10.95" id="M198" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>,如果<年代vg height="14.75" id="M199" style="vertical-align:-3.25793pt;width:57.049999px;" version="1.1" viewbox="0 0 57.049999 14.75" width="57.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.64,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.76,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> </g> </g> </svg>然后将失去稳定<年代vg height="10.95" id="M200" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>比<年代vg height="14.75" id="M201" style="vertical-align:-3.25793pt;width:78.212502px;" version="1.1" viewbox="0 0 78.212502 14.75" width="78.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.54,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.66,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.15,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>。</年代pan></p> <p><span class="statement" id="casee30"><span class="statement-title"><i class="statement-title">例3 (<年代vg height="14.75" id="M202" style="vertical-align:-3.25793pt;width:41.262501px;" version="1.1" viewbox="0 0 41.262501 14.75" width="41.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.0625" id="M203" style="vertical-align:-0.30096pt;width:39.237499px;" version="1.1" viewbox="0 0 39.237499 11.0625" width="39.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> 0</t年代pan> </text> </g> </g> </svg>)。</我></年代pan>再次,假设一个负面的<年代vg height="14.7125" id="M204" style="vertical-align:-3.22282pt;width:54.349998px;" version="1.1" viewbox="0 0 54.349998 14.7125" width="54.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.83,64.01)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>被选中,<年代vg height="12" id="M205" style="vertical-align:-0.1254pt;width:15.4875px;" version="1.1" viewbox="0 0 15.4875 12" width="15.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12)"> <g transform="translate(72,-62.4)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.74,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>是假定的延迟的大小。注意,如果<年代vg height="12.225" id="M206" style="vertical-align:-0.30096pt;width:43.887501px;" version="1.1" viewbox="0 0 43.887501 12.225" width="43.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.225)"> <g transform="translate(72,-62.22)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.01,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>,然后由图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig1/" target="_blank">1</一个>的<年代vg height="11.075" id="M207" style="vertical-align:-3.25793pt;width:14.0375px;" version="1.1" viewbox="0 0 14.0375 11.075" width="14.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>令人满意的<年代vg height="14.8625" id="M208" style="vertical-align:-3.25793pt;width:91.862503px;" version="1.1" viewbox="0 0 91.862503 14.8625" width="91.862503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.8,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.82,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.715311" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-3.43,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>更接近于<年代vg height="10.9125" id="M209" style="vertical-align:-0.17555pt;width:21.7875px;" version="1.1" viewbox="0 0 21.7875 10.9125" width="21.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.5893211" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="11.065155" y="0"> 2</t年代pan> </text> </g> </g> </svg>比<年代vg height="16.950001" id="M210" style="vertical-align:-4.35121pt;width:14.2875px;" version="1.1" viewbox="0 0 14.2875 16.950001" width="14.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.95)"> <g transform="translate(72,-58.44)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 0</t年代pan> </text> </g> </g> </svg>令人满意的<年代vg height="17.275" id="M211" style="vertical-align:-4.35121pt;width:96.099998px;" version="1.1" viewbox="0 0 96.099998 17.275" width="96.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.275)"> <g transform="translate(72,-58.18)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,59.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.8,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.59,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> <text transform="matrix(1,0,0,-1,-45.04,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.75,67.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.67,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="15.178642" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.24,67.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 0</t年代pan> </text> </g> </g> </svg>。因此<年代vg height="14.7125" id="M212" style="vertical-align:-3.22282pt;width:65.875px;" version="1.1" viewbox="0 0 65.875 14.7125" width="65.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.87,64.01)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ∗</t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.13,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊆</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>和反馈系统保持渐近稳定收益<年代vg height="10.325" id="M213" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。接下来,如果<年代vg height="13.4625" id="M214" style="vertical-align:-1.29163pt;width:43.887501px;" version="1.1" viewbox="0 0 43.887501 13.4625" width="43.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4625)"> <g transform="translate(72,-61.23)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.01,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>然后<年代vg height="14.7125" id="M215" style="vertical-align:-3.22282pt;width:60.662498px;" version="1.1" viewbox="0 0 60.662498 14.7125" width="60.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.9,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊆</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.79,64.01)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>和反馈系统保持渐近稳定当且仅当<年代vg height="10.95" id="M216" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>小于<年代vg height="14.75" id="M217" style="vertical-align:-3.25793pt;width:78.212502px;" version="1.1" viewbox="0 0 78.212502 14.75" width="78.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.54,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.66,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="17.254141" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.15,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="17.8375" id="M218" style="vertical-align:-3.25793pt;width:207.89999px;" version="1.1" viewbox="0 0 207.89999 17.8375" width="207.89999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8375)"> <g transform="translate(72,-57.73)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.35,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="17.579218" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> 年代</t年代pan> </text> <text transform="matrix(1,0,0,-1,-24.48,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-13.61,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,5.39,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,10.27,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.04303" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="27.206528" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="34.833359" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="46.873749" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="51.037247" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="57.288746" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="62.502499" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="70.104324" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="73.580154" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="79.831657" y="0"> )</t年代pan> </text> </g> </g> </svg>。</年代pan></p> <p><span class="statement" id="casee4"><span class="statement-title"><i class="statement-title">例4 (<年代vg height="14.75" id="M219" style="vertical-align:-3.25793pt;width:41.262501px;" version="1.1" viewbox="0 0 41.262501 14.75" width="41.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.0625" id="M220" style="vertical-align:-0.30096pt;width:39.237499px;" version="1.1" viewbox="0 0 39.237499 11.0625" width="39.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> 0</t年代pan> </text> </g> </g> </svg>)。</我></年代pan>因为积极的<年代vg height="14.7125" id="M221" style="vertical-align:-3.22282pt;width:49.637501px;" version="1.1" viewbox="0 0 49.637501 14.7125" width="49.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∉</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>对所有<年代vg height="10.95" id="M222" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>当<年代vg height="14.75" id="M223" style="vertical-align:-3.25793pt;width:41.262501px;" version="1.1" viewbox="0 0 41.262501 14.75" width="41.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>,这种情况下不需要讨论。</年代pan></p> <h5 id="sec5.3">5.3。响应性能</h5><p>与non-delay系统,系统频谱之前和之后的状态反馈稳定已经彻底研究[<一个href=”#B19">19</一个>,<一个href=”#B20">20.</一个>对时滞系统),相应的问题没有深入探索。假设它是所需的控制系统(<一个href=”#EEq2.1">1</一个>),这样的反应速度快但不振荡衰减率。在定理<一个href=”#thm2">5</一个>的范围,<年代vg height="10.325" id="M224" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>渐近稳定性的决定,但并不是每一个<年代vg height="10.325" id="M225" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>在<年代vg height="14.7125" id="M226" style="vertical-align:-3.22282pt;width:18.3375px;" version="1.1" viewbox="0 0 18.3375 14.7125" width="18.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>结果在一个比这更好的响应性能的控制系统。实际上,积极<年代vg height="11.075" id="M227" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>所有<年代vg height="14.7125" id="M228" style="vertical-align:-3.22282pt;width:49.637501px;" version="1.1" viewbox="0 0 49.637501 14.7125" width="49.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>提供了更好的性能,但不一定对于负面的<年代vg height="11.075" id="M229" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>。</p> <p><span class="statement" id="thm3"><span class="statement-title">定理7。</年代pan><i>对于系统(<一个href=”#EEq2.1">1</一个>),只有<年代vg height="14.8625" id="M230" style="vertical-align:-3.25793pt;width:151.85001px;" version="1.1" viewbox="0 0 151.85001 14.8625" width="151.85001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="29.194506" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="43.760502" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="37.771564" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.93,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-23.06,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="41.584976" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,24.77,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,29.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> )</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="14.75" id="M231" style="vertical-align:-3.25793pt;width:79.324997px;" version="1.1" viewbox="0 0 79.324997 14.75" width="79.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-65.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="-5.9889369" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.82,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="25.331078" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="19.34214" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.23,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.88,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M232" style="vertical-align:-3.25793pt;width:67.662498px;" version="1.1" viewbox="0 0 67.662498 14.75" width="67.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-65.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="-5.9889369" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.35,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.258461" y="0"> )</t年代pan> </text> </g> </g> </svg>,给一个更好的响应比控制系统的性能。</我></年代pan></p> <p><span class="statement" id="proof4"><span class="statement-title"><i class="statement-title">证明。</我></年代pan>假设为(<一个href=”#EEq2.1">1</一个>),<年代vg height="14.7125" id="M233" style="vertical-align:-3.22282pt;width:18.3375px;" version="1.1" viewbox="0 0 18.3375 14.7125" width="18.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>不是空的,<年代vg height="14.75" id="M234" style="vertical-align:-3.25793pt;width:41.262501px;" version="1.1" viewbox="0 0 41.262501 14.75" width="41.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>。从图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig2/" target="_blank">2</一个>,一组<年代vg height="14.7125" id="M235" style="vertical-align:-3.22282pt;width:18.3375px;" version="1.1" viewbox="0 0 18.3375 14.7125" width="18.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>包括三个子集<年代vg height="14.8625" id="M236" style="vertical-align:-3.25793pt;width:208.425px;" version="1.1" viewbox="0 0 208.425 14.8625" width="208.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.97,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.1,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.27,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.6,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="23.930742" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="17.941805" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,28.79,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,33.67,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="47.561413" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,81.49,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,86.36,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ]</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.8625" id="M237" style="vertical-align:-3.25793pt;width:120.55px;" version="1.1" viewbox="0 0 120.55 14.8625" width="120.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.97,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.1,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="41.584976" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.27,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.6,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> )</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.75" id="M238" style="vertical-align:-3.25793pt;width:61.200001px;" version="1.1" viewbox="0 0 61.200001 14.75" width="61.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="24.180801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-41.48,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3522444" y="0"> )</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="14.8625" id="M239" style="vertical-align:-3.25793pt;width:94.462502px;" version="1.1" viewbox="0 0 94.462502 14.8625" width="94.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.8,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.82,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.715311" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="19.34214" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.35,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.75" id="M240" style="vertical-align:-3.25793pt;width:79.324997px;" version="1.1" viewbox="0 0 79.324997 14.75" width="79.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-65.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="-5.9889369" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.82,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="25.331078" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="19.34214" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.23,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.88,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.75" id="M241" style="vertical-align:-3.25793pt;width:88.074997px;" version="1.1" viewbox="0 0 88.074997 14.75" width="88.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.82,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="11.202688" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-41.02,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.455387" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.258461" y="0"> )</t年代pan> </text> </g> </g> </svg><i>。</我>然而,只有<年代vg height="14.625" id="M242" style="vertical-align:-3.25793pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.625" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>对应于<年代vg height="14.8625" id="M243" style="vertical-align:-3.25793pt;width:151.85001px;" version="1.1" viewbox="0 0 151.85001 14.8625" width="151.85001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="29.194506" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="43.760502" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="37.771564" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.93,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-23.06,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="41.584976" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,24.77,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,29.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> )</t年代pan> </text> </g> </g> </svg>有负实部比<年代vg height="11.075" id="M244" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>,这意味着这样的反馈增益会导致一个更大的衰减率。接下来,设置<年代vg height="14.8625" id="M245" style="vertical-align:-3.25793pt;width:120.55px;" version="1.1" viewbox="0 0 120.55 14.8625" width="120.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.97,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.1,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="41.584976" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.27,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.6,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> )</t年代pan> </text> </g> </g> </svg>可分为<年代vg height="17.9125" id="M246" style="vertical-align:-3.25793pt;width:206.5125px;" version="1.1" viewbox="0 0 206.5125 17.9125" width="206.5125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.97,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.1,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="41.584976" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.27,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.6,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="17.929302" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,28.1,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,38.97,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,65.27,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,75.66,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,79.28,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,84.83,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="16.612499" id="M247" style="vertical-align:-2.21957pt;width:118.625px;" version="1.1" viewbox="0 0 118.625 16.612499" width="118.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.66,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.79,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.49,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.11,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-2.48,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,3.07,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> )</t年代pan> </text> </g> </g> </svg><i>,</我>在哪里<年代vg height="14.75" id="M248" style="vertical-align:-3.25793pt;width:79.324997px;" version="1.1" viewbox="0 0 79.324997 14.75" width="79.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-65.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="-5.9889369" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.82,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.702808" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="25.331078" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="19.34214" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-35.23,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.88,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M249" style="vertical-align:-3.25793pt;width:67.662498px;" version="1.1" viewbox="0 0 67.662498 14.75" width="67.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-65.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="-5.9889369" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.35,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.258461" y="0"> )</t年代pan> </text> </g> </g> </svg>。通过属性(ii),<年代vg height="14.625" id="M250" style="vertical-align:-3.25793pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.625" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>从<年代vg height="17.9125" id="M251" style="vertical-align:-3.25793pt;width:237.8px;" version="1.1" viewbox="0 0 237.8 17.9125" width="237.8" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="29.194506" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="43.760502" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="37.771564" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.93,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-23.06,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="22.805471" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.144974" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> ̃</t年代pan> <tspan style="font-size: 12.50px; " x="41.584976" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,24.77,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,29.64,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="17.929302" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,53.14,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,64.01,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,90.31,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,100.69,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,104.32,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,109.87,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代pan> </text> </g> </g> </svg>意味着一个振荡反应。最后,如果<年代vg height="16.612499" id="M252" style="vertical-align:-2.21957pt;width:149.925px;" version="1.1" viewbox="0 0 149.925 16.612499" width="149.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="29.194506" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.75906" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.62,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-17.75,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,8.54,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,18.93,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,22.56,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,28.1,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="15.62875" y="0"> )</t年代pan> </text> </g> </g> </svg>,然后<年代vg height="14.625" id="M253" style="vertical-align:-3.25793pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.625" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>是一个实值。虽然其他<年代vg height="14.5875" id="M254" style="vertical-align:-3.2316pt;width:15.1375px;" version="1.1" viewbox="0 0 15.1375 14.5875" width="15.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是复数,<年代vg height="14.625" id="M255" style="vertical-align:-3.25793pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.625" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>最右边的特征值,远离其他人。因此,振动只出现在瞬态响应。事实上,<年代vg height="16.612499" id="M256" style="vertical-align:-2.21957pt;width:125.1875px;" version="1.1" viewbox="0 0 125.1875 16.612499" width="125.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.78,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.91,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,4.38,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,14.77,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,18.39,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,23.94,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>给最大的衰变率和振荡。</年代pan></p> <h4 id="examples-and-simulations">6。例子和仿真</h4><p><span class="statement" id="ex1"><span class="statement-title"><i class="statement-title">示例8。</我></年代pan>我们的参数组合<年代vg height="14.8625" id="M257" style="vertical-align:-3.25793pt;width:168.6875px;" version="1.1" viewbox="0 0 168.6875 14.8625" width="168.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.291409" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.818695" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="62.077396" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="68.328896" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="73.542648" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="79.794144" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="85.007896" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="94.535187" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="99.736427" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="105.98793" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="109.11368" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="115.36518" y="0"> )</t年代pan> </text> </g> </g> </svg>被选中,<年代vg height="11.075" id="M258" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>不满足定理的条件<一个href=”#thm1">4</一个>,所以没有稳定收益<年代vg height="10.325" id="M259" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。校长轨迹和特征值<年代vg height="13.45" id="M260" style="vertical-align:-2.21957pt;width:87.987503px;" version="1.1" viewbox="0 0 87.987503 13.45" width="87.987503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="29.194506" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.75906" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="49.336838" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="54.550591" y="0"> ∞</t年代pan> <tspan style="font-size: 12.50px; " x="66.128365" y="0"> )</t年代pan> </text> </g> </g> </svg>如图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig3/" target="_blank">3</一个>,可以看出主要特征值总是位于右投手<年代vg height="10.325" id="M261" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是多少。</年代pan></p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="719730.fig.003" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.003.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/719730/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="10.325" id="M262" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <table> 校长轨迹和特征值。</t一个ble> </div> </div> </div> <p>然后考虑的参数组合<年代vg height="14.8625" id="M263" style="vertical-align:-3.25793pt;width:180.41251px;" version="1.1" viewbox="0 0 180.41251 14.8625" width="180.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.291409" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.818695" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="62.077396" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="68.328896" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="71.454643" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="77.706146" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="82.919899" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="89.171394" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="94.385147" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="103.91243" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="109.11368" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="115.36518" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="118.49093" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="124.74243" y="0"> )</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="14.8625" id="M264" style="vertical-align:-3.25793pt;width:54.625px;" version="1.1" viewbox="0 0 54.625 14.8625" width="54.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.33,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.767723" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>和存在一个可行集<年代vg height="14.925" id="M265" style="vertical-align:-3.22282pt;width:209.625px;" version="1.1" viewbox="0 0 209.625 14.925" width="209.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.9,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="37.83408" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.824696" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="62.865086" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="67.02858" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="75.59314" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="81.844635" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="84.97039" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="91.221886" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="97.473389" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="103.72489" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="109.97639" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="115.19014" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="123.75469" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="130.0062" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="133.13194" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="139.38344" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="143.54694" y="0"> }</t年代pan> </text> </g> </g> </svg>。在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig4/" target="_blank">4</一个>,一个反馈增益<年代vg height="14.7125" id="M266" style="vertical-align:-3.22282pt;width:49.637501px;" version="1.1" viewbox="0 0 49.637501 14.7125" width="49.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∉</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>使用,所以右投手和响应的主要特征值定位<年代vg height="13.45" id="M267" style="vertical-align:-2.21957pt;width:24.025px;" version="1.1" viewbox="0 0 24.025 13.45" width="24.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.953588" y="0"> )</t年代pan> </text> </g> </g> </svg>是不同的。在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig5/" target="_blank">5</一个>,一个反馈增益<年代vg height="14.7125" id="M268" style="vertical-align:-3.22282pt;width:49.637501px;" version="1.1" viewbox="0 0 49.637501 14.7125" width="49.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>使用,所以LHP和响应的主要特征值定位<年代vg height="13.45" id="M269" style="vertical-align:-2.21957pt;width:24.025px;" version="1.1" viewbox="0 0 24.025 13.45" width="24.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.953588" y="0"> )</t年代pan> </text> </g> </g> </svg>是收敛的。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”719730。f我g.004a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.004a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”719730。f我g.004b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.004b.jpg"> <br> <strong>(b)</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig4"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”719730。f我g.004a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.004a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”719730。f我g.004b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.004b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig4"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/719730/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#EEq2.2">2</一个><年代vg height="11.0375" id="M270" style="vertical-align:-0.27588pt" version="1.1" viewbox="0 0 69.474998 11.0375" width="69.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="39.847061" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="42.972813" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="49.224312" y="0"> 9</t年代pan> </text> </g> </g> </svg> <table> (一)特征值和(b)的反应系统(),。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”719730。f我g.005a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.005a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”719730。f我g.005b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.005b.jpg"> <br> <strong>(b)</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig5"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”719730。f我g.005a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.005a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”719730。f我g.005b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.005b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig5"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/719730/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#EEq2.2">2</一个><年代vg height="11.1" id="M271" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 61.662498 11.1" width="61.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="39.847061" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="42.972813" y="0"> 5</t年代pan> </text> </g> </g> </svg> <table> (一)特征值和(b)的反应系统(),。</t一个ble> </div> </div> </div> <p><span class="statement" id="ex2"><span class="statement-title"><i class="statement-title">示例9。</我></年代pan>在这个例子中,一个稳定<年代vg height="10.325" id="M272" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>测试系统的鲁棒性是固定的(<一个href=”#EEq2.2">2</一个>)对延迟时间<年代vg height="10.95" id="M273" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。有四个模拟。第一个是指的情况<一个href=”#casee10">1</一个>节<一个href=”#sec5.2">5.2</一个>,在那里<年代vg height="14.8625" id="M274" style="vertical-align:-3.25793pt;width:164.77499px;" version="1.1" viewbox="0 0 164.77499 14.8625" width="164.77499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.291409" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.818695" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="62.077396" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="70.641953" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="76.893448" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="82.107201" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="88.358704" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="93.572449" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="99.823952" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="105.0252" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="112.23943" y="0"> )</t年代pan> </text> </g> </g> </svg>,主要特征值对<年代vg height="10.95" id="M275" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>如图所示<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig6/" target="_blank">6(一)</一个>。这个系统的稳定性仿真是独立的<年代vg height="10.95" id="M276" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>。</年代pan></p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig6"> <div class="floats-partial-content fig-content-fig6"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”719730。f我g.006a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”719730。f我g.006b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006b.jpg"> <br> <strong>(b)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(c)”n一个米e=”719730。f我g.006c" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006c.jpg"> <br> <strong>(c)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(d)”n一个米e=”719730。f我g.006d" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006d.jpg"> <br> <strong>(d)</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig6"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”719730。f我g.006a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”719730。f我g.006b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006b.jpg"><br><strong>(b)</年代trong></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)”n一个米e=”719730。f我g.006c" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006c.jpg"><br><strong>(c)</年代trong></button> <button class="partial-carousel-dot" aria-label="(d)"><img alt="(d)”n一个米e=”719730。f我g.006d" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.006d.jpg"><br><strong>(d)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig6"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/719730/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#sec5.2">5.2</一个><我>:</我><一个href=”#casee10">1</一个><一个href=”#casee20">2</一个><一个href=”#casee20">2</一个><一个href=”#casee30">3</一个><t一个ble> 所有情况下的模拟部分(一)案例;(b)情况下(c);情况下;(d)情况下。</t一个ble> </div> </div> </div> <p>然后数据<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig6/" target="_blank">6 (b)</一个>和<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig6/" target="_blank">6 (c)</一个>参考案例<一个href=”#casee20">2</一个>节<一个href=”#sec5.2">5.2</一个>,<年代vg height="14.8625" id="M277" style="vertical-align:-3.25793pt;width:175.4875px;" version="1.1" viewbox="0 0 175.4875 14.8625" width="175.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.291409" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.818695" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="62.077396" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="70.641953" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="76.893448" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="82.107201" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="88.358704" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="93.572449" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="102.13701" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="108.3885" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="113.58975" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="120.80399" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.5625" id="M278" style="vertical-align:-2.21957pt;width:83.9375px;" version="1.1" viewbox="0 0 83.9375 13.5625" width="83.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="24.180801" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="30.432302" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="35.646053" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="44.210609" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="50.462109" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="55.663357" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="62.877586" y="0"> )</t年代pan> </text> </g> </g> </svg>,分别。在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig6/" target="_blank">6 (b)</一个>,这个系统的稳定性是依赖<我>h</我>,并仍然保持稳定<年代vg height="13.2375" id="M279" style="vertical-align:-1.95624pt;width:96.25px;" version="1.1" viewbox="0 0 96.25 13.2375" width="96.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.2375)"> <g transform="translate(72,-61.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="26.881451" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="33.13295" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="38.346703" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="44.598202" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="47.723949" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="53.975452" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="60.226952" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="66.478455" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="72.72995" y="0"> ]</t年代pan> </text> </g> </g> </svg>。在图<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig6/" target="_blank">6 (c)</一个>、稳定系统是独立的<我>h</我>。最后模拟指的情况<一个href=”#casee30">3</一个>节<一个href=”#sec5.2">5.2</一个>与<年代vg height="14.8625" id="M280" style="vertical-align:-3.25793pt;width:176.5px;" version="1.1" viewbox="0 0 176.5 14.8625" width="176.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.291409" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.818695" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="62.077396" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="68.328896" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="71.454643" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="77.706146" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="82.919899" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="89.171394" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="94.385147" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="102.9497" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="109.2012" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="114.40245" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="121.61668" y="0"> )</t年代pan> </text> </g> </g> </svg>。看到的是穿越频率为3.995,并仍然保持稳定<年代vg height="13.2375" id="M281" style="vertical-align:-1.95624pt;width:96.25px;" version="1.1" viewbox="0 0 96.25 13.2375" width="96.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.2375)"> <g transform="translate(72,-61.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.717951" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="26.881451" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="33.13295" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="38.346703" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="44.598202" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="47.723949" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="53.975452" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="60.226952" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="66.478455" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="72.72995" y="0"> ]</t年代pan> </text> </g> </g> </svg>。</p> <p><span class="statement" id="ex3"><span class="statement-title"><i class="statement-title">示例10。</我></年代pan>我们的参数组合<年代vg height="14.9375" id="M282" style="vertical-align:-3.25793pt;width:211.66251px;" version="1.1" viewbox="0 0 211.66251 14.9375" width="211.66251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.64,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.291409" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.818695" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="62.077396" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="68.328896" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="71.454643" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="77.706146" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="83.957642" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="89.171394" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="95.422897" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="98.548645" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="104.80015" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="111.05164" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="117.30315" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="123.55465" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="128.7684" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="138.29568" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="143.49693" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="149.74843" y="0"> )</t年代pan> </text> </g> </g> </svg>(<一个href=”#B21">21</一个>被选中。的参数<年代vg height="11.075" id="M283" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>是积极和满足定理呢<一个href=”#thm1">4</一个>,<年代vg height="14.925" id="M284" style="vertical-align:-3.22282pt;width:233.075px;" version="1.1" viewbox="0 0 233.075 14.925" width="233.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.9,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="37.83408" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.824696" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="62.865086" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="67.02858" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="75.59314" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="81.844635" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="84.97039" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="91.221886" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="97.473389" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="103.72489" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="109.97639" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="115.19014" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="123.75469" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="130.0062" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="133.13194" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="139.38344" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="145.63495" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="151.88644" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="158.13794" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="162.30144" y="0"> }</t年代pan> </text> </g> </g> </svg>。在这个例子中,所有<年代vg height="14.7125" id="M285" style="vertical-align:-3.22282pt;width:49.637501px;" version="1.1" viewbox="0 0 49.637501 14.7125" width="49.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> </g> </g> </svg>给更好的闭环系统响应性能。为<年代vg height="11.0375" id="M286" style="vertical-align:-0.17555pt;width:85.112503px;" version="1.1" viewbox="0 0 85.112503 11.0375" width="85.112503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="39.847061" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="42.972813" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="49.224312" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="55.475811" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="61.72731" y="0"> 7</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.0375" id="M287" style="vertical-align:-0.27588pt;width:77.287498px;" version="1.1" viewbox="0 0 77.287498 11.0375" width="77.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="39.847061" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="42.972813" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="49.224312" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="55.475811" y="0"> 9</t年代pan> </text> </g> </g> </svg>,对应于<年代vg height="14.9375" id="M288" style="vertical-align:-3.25793pt;width:87.75px;" version="1.1" viewbox="0 0 87.75 14.9375" width="87.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="29.96969" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="36.221191" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="42.472691" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="48.72419" y="0"> 7</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.875" id="M289" style="vertical-align:-3.25793pt;width:87.75px;" version="1.1" viewbox="0 0 87.75 14.875" width="87.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.875)"> <g transform="translate(72,-60.1)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="29.96969" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="36.221191" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="42.472691" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="48.72419" y="0"> 3</t年代pan> </text> </g> </g> </svg>分别如图的响应<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig7/" target="_blank">7(一)</一个>,蓝线(<年代vg height="16.612499" id="M290" style="vertical-align:-2.21957pt;width:125.175px;" version="1.1" viewbox="0 0 125.175 16.612499" width="125.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.78,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.91,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.37,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,14.76,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,18.38,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,23.93,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>)比绿线的衰减率。考虑另一个参数组合<年代vg height="14.8625" id="M291" style="vertical-align:-3.25793pt;width:179.39999px;" version="1.1" viewbox="0 0 179.39999 14.8625" width="179.39999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.291409" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.818695" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="62.077396" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="70.641953" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="76.893448" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="82.107201" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="88.358704" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="93.572449" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="103.09974" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="108.30099" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="114.55248" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="117.67824" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="123.92973" y="0"> )</t年代pan> </text> </g> </g> </svg>。的参数<年代vg height="11.075" id="M292" style="vertical-align:-3.25793pt;width:14.0625px;" version="1.1" viewbox="0 0 14.0625 11.075" width="14.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>是负和满足定理<一个href=”#thm1">4</一个>,<年代vg height="14.925" id="M293" style="vertical-align:-3.22282pt;width:233.075px;" version="1.1" viewbox="0 0 233.075 14.925" width="233.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.9,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.032446" y="0"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="37.83408" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.824696" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="62.865086" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="67.02858" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="75.59314" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="81.844635" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="84.97039" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="91.221886" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="97.473389" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="103.72489" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="109.97639" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="115.19014" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="123.75469" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="130.0062" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="133.13194" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="139.38344" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="145.63495" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="151.88644" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="158.13794" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="162.30144" y="0"> }</t年代pan> </text> </g> </g> </svg>。对于这种情况只<年代vg height="13.45" id="M294" style="vertical-align:-2.21957pt;width:102.025px;" version="1.1" viewbox="0 0 102.025 13.45" width="102.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="29.194506" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.75906" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="44.010559" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="47.136311" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="53.38781" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="59.639309" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="65.890808" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="71.104561" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="77.356064" y="0"> )</t年代pan> </text> </g> </g> </svg>产生一个更好的闭环响应性能。对三种不同的收益<我>K</我>=- 0.37461,<年代vg height="11.0375" id="M295" style="vertical-align:-0.27588pt;width:95.525002px;" version="1.1" viewbox="0 0 95.525002 11.0375" width="95.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="27.119007" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="35.683563" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="41.935062" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="45.060814" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="51.312313" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="57.563812" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="63.815311" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="70.066811" y="0"> 9</t年代pan> </text> </g> </g> </svg>,<年代vg height="11.1" id="M296" style="vertical-align:-0.17555pt;width:100.7375px;" version="1.1" viewbox="0 0 100.7375 11.1" width="100.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="39.847061" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="42.972813" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="49.224312" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="55.475811" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="61.72731" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="67.978813" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="74.230309" y="0"> 2</t年代pan> </text> </g> </g> </svg>相应的,<年代vg height="14.9375" id="M297" style="vertical-align:-3.25793pt;width:191.21249px;" version="1.1" viewbox="0 0 191.21249 14.9375" width="191.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="29.96969" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="39.009361" y="0"> ±</t年代pan> <tspan style="font-size: 12.50px; " x="50.349583" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="56.601082" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="59.72683" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="65.978333" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="72.229828" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="78.481331" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="84.732834" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="89.596497" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="94.810249" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="103.3748" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="109.6263" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="112.75205" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="119.00356" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="125.25505" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="131.50656" y="0"> 6</t年代pan> </text> </g> </g> </svg>分别和−1.4图所示的响应<一个href=”//www.newsama.com/journals/jcse/2011/719730/fig7/" target="_blank">7 (b)</一个>,蓝色和红色线有相同的衰减率,但蓝线振荡。此外,绿线是最好的,因为<年代vg height="16.612499" id="M298" style="vertical-align:-2.21957pt;width:206.075px;" version="1.1" viewbox="0 0 206.075 16.612499" width="206.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.595562" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.78,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.91,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="20.729975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,4.38,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,14.77,63.78)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,18.39,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代pan> </text> <text transform="matrix(1,0,0,-1,23.94,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.231773" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="34.483273" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="37.609024" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="43.860523" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="50.112022" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="56.363525" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="62.615025" y="0"> 9</t年代pan> </text> </g> </g> </svg>。</年代pan></p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig7"> <div class="floats-partial-content fig-content-fig7"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”719730。f我g.007a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.007a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”719730。f我g.007b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.007b.jpg"> <br> <strong>(b)</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig7"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”719730。f我g.007a" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.007a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”719730。f我g.007b" src="https://static-01.hindawi.com/articles/jcse/volume-2011/719730/figures/719730.fig.007b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig7"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/719730/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#ex3">10</一个><t一个ble> 反应的例子。</t一个ble> </div> </div> </div> <h4 id="conclusions">7所示。结论</h4><p>低阶时滞系统在化学工程应用非常普遍,本文研究的光谱一阶线性时滞系统通过兰伯特的功能。讨论了这种系统的稳定性和稳定特征值的方法。通过专注于主要的特征值,获得稳定收益的间隔,和一个固定的稳定增加,系统的稳定鲁棒性对延迟时间探讨。此外,通过光谱的充分理解,如何决定反馈增益获得更好的性能响应进行了探讨。三个例子显示和模拟演示派生的结果。</p> <p>尽管本文只着重于一阶系统,可以讨论高阶系统分析的基础上本文利用部分分式扩张的方法。这将是未来工作的调查目标。</p> <h4 id="acknowledgment">承认</h4><p>这项研究是由美国国家科学委员会中华民国在格兰特NSC - 002 - 148 - 98 - 2221 e my3。</p> </div> <div class="xml-content"> <h4 class="references" id="references">引用</h4><ol> <li id="B1">顾k、v . l . 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height="24"><span class="text">引用</年代pan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cTjmhe ihmyEq article_bottom_toolbar"> <div class="sc-cugefK itFKcQ accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</年代pan><span class="sc-gkFcWv gWTCXQ">更多的</年代pan></span> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/jcse/2011/719730.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> ePub</div><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">订单打印副本</年代pan><span class="sc-gkFcWv gWTCXQ">订单</年代pan></span><span class="sc-htoDjs kNoiZu sc-gbOuXE jGPvPL right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-hBbWxd kdRRST"> <div class="sc-dyGzUR cHatnS"> <div> 的观点<年代pan>3231年</年代pan> </div> <div> 下载<年代pan>914年</年代pan> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2011/719730" data-style="small_circle"></span>引用</div> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</h3><ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2011/719730&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" role="presentation" 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