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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .ejdfnh .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){.ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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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){.ejdfnh .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){.ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .ejdfnh .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .ejdfnh ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .ejdfnh ol li{margin:10px 0;padding-left:10px;word-break:normal;} .ejdfnh ol li a{word-break:break-all;} .ejdfnh ol li .reflinks{display:block;} .ejdfnh ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .ejdfnh ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .ejdfnh ol li .reflinks .sep{color:#000000;} .ejdfnh .table-wrapper{width:auto;overflow-x:auto;} .ejdfnh .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .ejdfnh .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 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svg{fill:#007B8B;} .ejdfnh .floats-partial-middle--thumbs .partial-carousel-dot .nowrap{white-space:nowrap;} .ejdfnh .partial-carousel-dot{text-align:center;cursor:pointer;border:0;width:100px;padding-bottom:20px;background-color:#fff;display:table-cell;} .ejdfnh .partial-carousel-dot:focus-visible{outline-offset:-3px;} .ejdfnh .partial-carousel-dot strong{font-size:11px;padding-top:12px;} @media (min-width:767.5px){.ejdfnh .partial-carousel-dot strong{font-size:16px;}} .ejdfnh .partial-carousel-dot img{width:90px;height:90px;border:1px solid #979797;margin:10px 0;} .ejdfnh .partial-carousel-wrapper .floats-partial-middle{border-top:1px solid #e3e3e3;display:block;margin-bottom:50px;padding-top:1px;} @media (min-width:767.5px){.ejdfnh .partial-carousel-wrapper .floats-partial-middle{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;margin-bottom:0;}} .ejdfnh .partial-carousel--single-image{overflow:hidden;text-align:center;} .ejdfnh 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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>/<gydF4y2Ba一个class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jcse/contents/year/2012/" aria-label="2012">2012年</一个>/<gydF4y2Ba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</gydF4y2Babutton> <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</gydF4y2Bap> <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="#numerical-example" aria-label="">数值例子</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|<gydF4y2Ba!-- -->开放获取</gydF4y2Bap> <div class="sc-RcBXQ ztvYg article_citation"> 体积<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</年代pan>文章的ID<gydF4y2Ba!-- --> 564906年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</年代pan> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2012/564906" aria-label="Doi-link">https://doi.org/10.1155/2012/564906</一个></d我v> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>Jeang-Lin常<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> ”<年代pan class="adjust-article-svg-size">Chattering-Free动态滑模控制器的设计</年代pan>”,<gydF4y2Ba!-- --><i>控制科学与工程》杂志上</我>,<ggydF4y2BaydF4y2Ba!-- --> 卷。<gydF4y2Ba!-- -->2012年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 文章的ID<gydF4y2Ba!-- -->564906年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 7<gydF4y2Ba!-- -->   页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- --> https://doi.org/10.1155/2012/564906</gydF4y2Bap> </div> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</gydF4y2Babutton> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN kmVdUp article_title adjust-article-svg-size heading-title">Chattering-Free动态滑模控制器的设计</gydF4y2Bah1> </div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class=""><b>Jeang-Lin常</gydF4y2Bab><a 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>电气工程系,东方理工学院,工前,新220年台北市,台湾</年代pan></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</gydF4y2Babutton> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</gydF4y2Bab>庸陈</d我v> <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">07年6月2012年</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">07年8月2012年</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">08年8月2012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">06年9月2012年</年代pan> </div> </div> </div> <article class="sc-jtRlXQ ejdfnh article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</gydF4y2Bah4> <p>针对一类线性不确定系统,动态滑模控制算法,避免了抖振问题是提出了。没有使用任何的区别,我们开发一个修改后的渐近稳定的二阶滑模控制律提出控制器能保证滑模的有限时间收敛,可以显示系统状态渐近方法为零。最后,数值例子说明来论证该方案的适用性。</gydF4y2Bap> <span class="end-abs"></span> <h4 id="introduction">1。介绍</gydF4y2Bah4> <p>滑模控制(SMC)已经成功地用于许多不确定控制系统(<一个href="#B1">1</一个>,<gydF4y2Ba一个href="#B2">2</一个>]。系统匹配的干扰,SMC可以获得完美的在滑模干扰抑制。控制目标是实现通过约束系统动力学在正确选择滑动变量通过不连续控制律。理论上,SMC提供鲁棒稳定性与无限的快速交换系统通过高增益控制行动。然而,高增益控制设计受到峰值现象的缺点,在控制输入峰值在瞬态阶段一个极大值。峰值现象可以很容易地控制饱和约束违反。SMC方案往往是不连续和反馈控制输入需要与无限的开关切换频率。不连续的高速转换作用导致固有的抖振问题由于延迟和其他问题(<一个href="#B1">1</一个>,<gydF4y2Ba一个href="#B2">2</一个>]。喋喋不休的行动可能刺激未建模动态高阶,这可能导致不可预见的不稳定(<一个href="#B1">1</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B5">5</一个>]。有两个主要方法报道应对喋喋不休的问题。第一个方法是插入一个固定或可变边界层附近滑动变量(<一个href="#B6">6</一个>),这样一个连续控制取代了不连续当边界层内的系统之一。另一种消除抖振的方法是由增加一个辅助控制输入到系统,比如使用模糊控制的<一个href="#B7">7</一个>,<gydF4y2Ba一个href="#B8">8</一个>和自适应模糊控制<一个href="#B9">9</一个>]。这些提到的方法(<一个href="#B1">1</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B5">5</一个>可以给chattering-free系统,但一个有限的可能存在稳态误差。因此,完善的抗干扰性无法保证的财产。</gydF4y2Bap> <p>动态滑模控制(<一个href="#B10">10</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B14">14</一个>前),使用一个积分器系统是一种特殊的方法来消除控制嚷嚷起来。控制输入的时间导数作为新的控制变量的增广系统增广系统包括原系统和积分器。因为没有边界层用于控制器,一个动态滑模控制器的优点是减少聊天是通过使用一个积分器和完美的抗干扰性保证的财产。因此,动态滑模控制不仅消除了一些基本的传统方法的局限性,但也提供了改进的滑模跟踪精度。的主要问题实现动态滑模控制器是日益增长的信息需求,滑动变量的导数的知识是必需的。Bartolini et al。<一个href="#B11">11</一个>,<gydF4y2Ba一个href="#B12">12</一个>)提出了一种次优版本的扭曲算法(<一个href="#B15">15</一个>,<gydF4y2Ba一个href="#B16">16</一个>)应对喋喋不休的问题。然而,这种方法需要至少的知识滑动变量的导数的符号。陈等人。<一个href="#B14">14</一个>应用一个LTR观察者克服滑动变量估计的问题。最近,黎凡特(<一个href="#B15">15</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B17">17</一个>]给出了扭曲算法稳定二阶非线性系统,但需要滑动变量的导数的知识。超级扭曲算法(<一个href="#B15">15</一个>,<gydF4y2Ba一个href="#B16">16</一个>)不需要输出的导数测量但它最初开发和分析了系统相对程度。黎凡特(<一个href="#B17">17</一个>]提出一个精确的有限时间收敛的区别可以成功地估计滑动变量的导数,但需要先验界轨迹。</gydF4y2Bap> <p>针对线性MIMO系统匹配的干扰,另一种动态滑模控制器避免了抖振问题是建立。我们首先提出一个修改后的二阶滑模控制方法来稳定摄动系统。引入滑动变量的一个比例积分项和一个积分符号函数项控制律,结果部队chattering-free控制。基于发达二阶滑模技术,结果表明,滑模的有限时间收敛性提供了理论上和零稳态误差可以保证通过应用该控制律。因此,执行的控制精度比那些传统的边界层控制(<一个href="#B3">3</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B5">5</一个>]。此外,闭环稳定的一个充分条件,提出了控制算法的实现很简单。与传统的动态滑模控制器(<一个href="#B10">10</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B14">14</一个>),该方法不需要任何观察者结构估算滑动变量的导数。最后,说明了该方法的可行性,一个数值例子。</gydF4y2Bap> <p>本文的组织如下。部分<一个href="#sec2">2</一个>描述了一类不确定线性系统,给出了问题公式化。部分<一个href="#sec3">3</一个>提出了修改后的二阶滑模方法和发展动态滑模控制器设计。仿真结果中包含部分<一个href="#sec4">4</一个>。部分<一个href="#sec5">5</一个>提供了一个简短的结论。</gydF4y2Bap> <h4 id="problem-formulation">2。问题公式化</gydF4y2Bah4> <p>考虑一个系统满足匹配条件的不确定的形式<年代pan class="equation" id="EEq1"> <svg height="16.5375" id="M1" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" 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y="0.14"> +</t年代pan> <tspan style="font-size: 12.50px; " x="74.176765" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="84.591766" y="0.14"> (</t年代pan> <tspan style="font-size: 12.50px; " x="88.755264" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="97.794937" y="0.14"> (</t年代pan> <tspan style="font-size: 12.50px; " x="101.95844" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="105.87187" y="0.14"> )</t年代pan> <tspan style="font-size: 12.50px; " x="112.81104" y="0.14"> +</t年代pan> <tspan style="font-size: 12.50px; " x="124.16376" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="133.19093" y="0.14"> (</t年代pan> <tspan style="font-size: 12.50px; " x="137.35443" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="141.26787" y="0.14"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="146.48161" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="152.98318" y="0.14"> )</t年代pan> <tspan style="font-size: 12.50px; " x="157.14668" y="0.14"> )</t年代pan> <tspan style="font-size: 12.50px; " x="163.39818" y="0.14"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="344.89999" y="0.76999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="349.06351" y="0.76999998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="355.315" y="0.76999998"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="11.625" id="M2" style="vertical-align:-0.33858pt;width:45.0625px;" version="1.1" viewbox="0 0 45.0625 11.625" width="45.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.625)"> <g transform="translate(72,-62.7)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <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"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.85,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>状态向量,<年代vg height="11.625" id="M3" style="vertical-align:-0.33858pt;width:48.262501px;" version="1.1" viewbox="0 0 48.262501 11.625" width="48.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.625)"> <g transform="translate(72,-62.7)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="22.455387" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.15,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>是控制输入向量,<年代vg height="14.4" id="M4" style="vertical-align:-2.5707pt;width:44.974998px;" version="1.1" viewbox="0 0 44.974998 14.4" width="44.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4)"> <g transform="translate(72,-60.48)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <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"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.85,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>是输出向量,然后呢<年代vg height="11.625" id="M5" style="vertical-align:-0.33858pt;width:48.262501px;" version="1.1" viewbox="0 0 48.262501 11.625" width="48.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.625)"> <g transform="translate(72,-62.7)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="22.455387" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.15,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>是与已知上界未知扰动向量匹配<年代vg height="14.8125" id="M6" style="vertical-align:-3.13504pt;width:88.112503px;" version="1.1" viewbox="0 0 88.112503 14.8125" width="88.112503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="13.490737" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="17.654236" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="21.567675" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="26.768923" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="33.020424" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="37.183922" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="47.198826" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="59.239216" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.43,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="17.2875" id="M7" style="vertical-align:-3.13504pt;width:88.112503px;" version="1.1" viewbox="0 0 88.112503 17.2875" width="88.112503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.2875)"> <g transform="translate(72,-58.17)"> <text transform="matrix(1,0,0,-1,-71.95,61.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="14.42" y="-2.8199999"></tspan> <tspan style="font-size: 12.50px; " x="6.54" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="13.491668" y="7.1054274e-015"> (</t年代pan> <tspan style="font-size: 12.50px; " x="17.655167" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="21.568605" y="7.1054274e-015"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="26.769854" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="33.021355" y="7.1054274e-015"> )</t年代pan> <tspan style="font-size: 12.50px; " x="37.184853" y="7.1054274e-015"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="47.199757" y="7.1054274e-015"> =</t年代pan> <tspan style="font-size: 12.50px; " x="59.240147" y="7.1054274e-015"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.43,58.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>。假设系统的状态可以被测量和对<年代vg height="13.675" id="M8" style="vertical-align:-2.21957pt;width:38.75px;" version="1.1" viewbox="0 0 38.75 13.675" width="38.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.675)"> <g transform="translate(72,-61.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <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="13.190665" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="18.391912" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="26.731415" y="0"> )</t年代pan> </text> </g> </g> </svg>稳定化。让被选为滑动变量<年代pan class="equation" id="EEq2"> <svg height="16.5375" id="M9" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" 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,-1,174.19,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.016103" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="22.655436" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="34.683323" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="44.410656" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="53.000217" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="57.163715" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="61.077156" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="67.328651" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="299.92999" y="0.63"> (</t年代pan> <tspan style="font-size: 12.50px; " x="304.09351" y="0.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="310.345" y="0.63"> )</t年代pan> </text> </g> </g> </svg></span>的矩阵<年代vg height="12.5875" id="M10" style="vertical-align:-0.33858pt;width:64.175003px;" version="1.1" viewbox="0 0 64.175003 12.5875" width="64.175003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.5875)"> <g transform="translate(72,-61.93)"> <text transform="matrix(1,0,0,-1,-71.95,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="25.231054" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.37,67.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="11.8152" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>旨在稳定降维体系。满足达到和滑动条件下,常规的控制输入设计滑模控制器<年代pan class="equation" id="EEq3"> <svg height="18.9" id="M11" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.9" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.9)"> <g transform="translate(72,-56.88)"> <text transform="matrix(1,0,0,-1,101.93,60.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</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="17.104103" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.743437" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="36.771324" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="45.335876" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="49.499378" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="59.226711" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="67.566216" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,173.67,66.03)"> <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,-1,186.63,60.68)"> <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="13.890833" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="31.495056" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="35.658558" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="39.571995" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="46.511162" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="57.851379" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="66.290909" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="71.154572" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="74.630409" y="0"> g</t年代pan> <tspan style="font-size: 12.50px; " x="80.881905" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="93.384911" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="97.548409" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="104.50008" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="108.66357" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="112.57701" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="116.74051" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="120.90401" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="127.14301" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="287.48999" y="-0.63"> (</t年代pan> <tspan style="font-size: 12.50px; " x="291.6535" y="-0.63"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="297.905" y="-0.63"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="13.6125" id="M12" style="vertical-align:-2.34499pt;width:35.262501px;" version="1.1" viewbox="0 0 35.262501 13.6125" width="35.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <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="9.8148546" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="21.855244" y="0"> 0</t年代pan> </text> </g> </g> </svg>是一个高增益设计这样的系统达到和幻灯片在有限时间滑动变量。然而,这种现象称为喋喋不休是由于不连续函数中生成的<年代vg height="14.2" id="M13" style="vertical-align:-2.73372pt;width:63.174999px;" version="1.1" viewbox="0 0 63.174999 14.2" width="63.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <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"> g</t年代pan> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="29.169498" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="34.033165" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="38.196667" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="42.110104" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> )</t年代pan> </text> </g> </g> </svg>。它可以被视为不受欢迎的抖振效应产生的高转换作用的控制输入。因此,SMC的聊天变成了主要的实现问题。众多技术提出了消除这一现象在SMC (<一个href="#B3">3</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B14">14</一个>]。最常见的一种解决方案来减少震颤是边界层技术(<一个href="#B3">3</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B5">5</一个>]。然而,边界层厚度之间的权衡关系控制性能,而聊天的迁移。另一个缺点,应用边界层方法(<一个href="#B3">3</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B5">5</一个>控制精度的降低。</gydF4y2Bap> <p>针对线性MIMO系统匹配的干扰,在本文中,我们提出一个动态滑模控制算法的提出过程可以有效降低抖振效应。我们首先开发一个修改后的二阶滑模控制方法稳定摄动系统。滑动变量的引入比例积分项和一个积分符号函数项到控制器中,滑模的有限时间收敛性保证了应用开发的二阶滑模技术。此外,系统的所有状态渐近方法为零,一旦系统在滑模。</gydF4y2Bap> <h4 id="dynamic-sliding-mode-controller-design">3所示。动态滑模控制器设计</gydF4y2Bah4> <p>在本节中,我们提出一个动态滑模控制算法可以成功地避免喋喋不休的线性分布式天线系统匹配的干扰。修改后的二阶滑模控制算法,它不需要滑动变量的导数。该控制律能保证滑模的有限时间收敛和稳定的降维系统系统状态渐近方法为零。</gydF4y2Bap> <p>滑动的变量(<一个href="#EEq2">2</一个>),我们设计的动态滑模控制器<年代pan class="equation" id="EEq4"> <svg height="89.4375" id="M14" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 89.4375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,89.4375)"> <g transform="translate(72,-0.45)"> <text transform="matrix(1,0,0,-1,75.09,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</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="17.104103" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.743437" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="40.259659" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="51.59988" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="55.763378" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="65.490715" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="73.830215" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,153.09,58.32)"> <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,-1,166.04,45.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="9.3800001" y="-7.3299999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="19.107334" y="-7.3299999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="28.134501" y="-7.3299999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="36.711559" y="-7.3299999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="40.875057" y="-7.3299999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="44.788494" y="-7.3299999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="51.727661" y="-7.3299999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="63.080383" y="-7.3299999"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,237.46,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,242.33,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.115167" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.028606" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="21.967772" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="33.307991" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,283.98,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,290.94,45.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> </text> <text transform="matrix(1,0,0,-1,297.94,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,303.65,52.96)"> <tspan style="font-size: 12.50px; " x="-117.61" y="47.91"> 吗?</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="6.9391651" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.5042" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="23.755699" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="30.407295" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-137.98" y="40.209999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-129.41545" y="40.209999"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,193.04,26.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,198.75,12.75)"> <tspan style="font-size: 12.50px; " x="72.239998" y="7.3299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="83.699997" y="0"> ,</t年代pan> <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"> g</t年代pan> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="27.094002" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="31.2575" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="38.196667" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="48.7617" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="52.925198" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="59.176701" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="65.828293" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="275.37" y="-20.35"> (</t年代pan> <tspan style="font-size: 12.50px; " x="279.53351" y="-20.35"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="285.785" y="-20.35"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="16.075001" id="M15" style="vertical-align:-3.13504pt;width:70.862503px;" version="1.1" viewbox="0 0 70.862503 16.075001" width="70.862503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.075)"> <g transform="translate(72,-59.14)"> <text transform="matrix(1,0,0,-1,-71.95,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.61,59.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-55.26,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.89,67.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="11.8152" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>,<年代vg height="16.075001" id="M16" style="vertical-align:-3.13504pt;width:70.862503px;" version="1.1" viewbox="0 0 70.862503 16.075001" width="70.862503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.075)"> <g transform="translate(72,-59.14)"> <text transform="matrix(1,0,0,-1,-71.95,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.61,59.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-55.26,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.89,67.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="11.8152" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>,<年代vg height="12.5875" id="M17" style="vertical-align:-0.33858pt;width:66.512497px;" version="1.1" viewbox="0 0 66.512497 12.5875" width="66.512497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.5875)"> <g transform="translate(72,-61.93)"> <text transform="matrix(1,0,0,-1,-71.95,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="25.231054" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.37,67.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="11.8152" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>的正定对角矩阵吗<年代pan class="equation" id="EEq5"> <svg height="49.775002" id="M18" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.775002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.775)"> <g transform="translate(72,-32.18)"> <text transform="matrix(1,0,0,-1,61.73,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,70.07,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,78.42,61.13)"> <tspan style="font-size: 12.50px; " x="39.82" y="2.51"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.669998" 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="12.027886" y="0"> d</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="27.306553" y="0"> g</t年代pan> </text> <text transform="matrix(1,0,0,-1,128.07,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,137.32,61.13)"> <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="19.79225" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,166.3,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,177.39,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="33.061031" y="-2.51"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,218.8,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.15,61.13)"> <tspan style="font-size: 12.50px; " x="39.82" y="2.51"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.669998" 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="12.027886" y="0"> d</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="27.306553" y="0"> g</t年代pan> </text> <text transform="matrix(1,0,0,-1,276.79,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,286.04,61.13)"> <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="19.79225" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,315.03,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,326.11,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-123.71" y="24.34"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-117.86" y="21.83"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-176.73" y="21.83"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-163.53934" y="21.83"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-151.49895" y="21.83"> d</t年代pan> <tspan style="font-size: 12.50px; " x="-145.24745" y="21.83"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="-141.77161" y="21.83"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="-136.22028" y="21.83"> g</t年代pan> </text> <text transform="matrix(1,0,0,-1,215.03,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,219.9,36.79)"> <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="19.79225" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,251.68,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.4,34.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="215.72" y="-14.68"> (</t年代pan> <tspan style="font-size: 12.50px; " x="219.8835" y="-14.68"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="226.13499" y="-14.68"> )</t年代pan> </text> </g> </g> </svg></span>花时间的导数(<一个href="#EEq2">2</一个>控制输入()和替换<一个href="#EEq4">4</一个>它能获得)<年代pan class="equation" id="EEq6"> <svg height="92.0625" id="M19" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 92.0625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,92.0625)"> <g transform="translate(72,1.65)"> <text transform="matrix(1,0,0,-1,77.8,63.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="45.959999" y="0.15000001"></tspan> <tspan style="font-size: 12.50px; " x="-5.29" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="1.649165" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="5.812664" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.7261028" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.365437" y="0.28999999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.093491" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="39.830002" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="48.407059" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="52.570557" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="56.483997" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="64.123329" y="0.28999999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="76.163719" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="85.891052" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="94.918221" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="103.49528" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="107.65878" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="111.57221" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="118.52388" y="0.28999999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="129.86411" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="139.59143" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="150.00644" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="154.16994" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="163.20961" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="167.37311" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="171.28654" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="178.22571" y="0.28999999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="189.57843" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="198.60559" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="202.76909" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="206.68254" y="0.28999999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="211.89629" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="218.39784" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="222.56134" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.370001" y="32"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.873718" y="32"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="44.21394" y="32"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,130.36,28.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,135.24,31.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.016103" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="21.955269" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="33.29549" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.89,28.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.84,23.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.85,45.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,196.55,31.49)"> <tspan style="font-size: 12.50px; " x="62.75" y="7.6999998"> 吗?</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="6.9391651" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.5042" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="23.755699" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="30.407295" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="39.584499" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="50.937222" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,266.3,45.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,272.01,31.49)"> <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"> g</t年代pan> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="27.081497" y="0"> (</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="38.196667" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="48.7617" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="52.925198" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="59.176701" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="65.828293" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-161.33" y="29.34"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-149.98978" y="29.34"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-140.26245" y="29.34"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-131.92294" y="29.34"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-122.89577" y="29.34"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-118.73228" y="29.34"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-114.81884" y="29.34"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-109.60509" y="29.34"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-103.10353" y="29.34"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-96.852028" y="29.34"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="202.11" y="-0.56"> (</t年代pan> <tspan style="font-size: 12.50px; " x="206.2735" y="-0.56"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="212.52499" y="-0.56"> )</t年代pan> </text> </g> </g> </svg></span>进一步区分(<一个href="#EEq6">6</一个>)随着时间的收益率以下动态:<年代pan class="equation" id="EEq7"> <svg height="16.5375" id="M20" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" 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,-1,93.81,63.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-5.29" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="1.649165" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="5.812664" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.7261028" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="16.665268" y="0.28999999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.005489" y="0.28999999"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,130.17,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,140.33,63.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-5.29" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="1.649165" y="0.28999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="5.812664" y="0.28999999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.7261028" y="0.28999999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="16.665268" y="0.28999999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.017992" y="0.28999999"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.69,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,181.56,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.115167" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.028606" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="22.655436" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="34.695824" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="43.26038" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="55.075714" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="59.939381" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="63.415215" y="0"> g</t年代pan> <tspan style="font-size: 12.50px; " x="69.666718" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="82.169716" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="86.333214" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="93.272377" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="97.435883" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="101.34932" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="105.51282" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="112.46449" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="123.8047" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="131.3065" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="135.47" y="0"> ? ?</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="145.62244" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="292.56" y="0.63"> (</t年代pan> <tspan style="font-size: 12.50px; " x="296.72351" y="0.63"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="302.97501" y="0.63"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="17.6" id="M21" style="vertical-align:-3.20526pt;width:235.28751px;" version="1.1" viewbox="0 0 235.28751 17.6" width="235.28751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.6)"> <g transform="translate(72,-57.92)"> <text transform="matrix(1,0,0,-1,-71.95,61.17)"> <tspan style="font-size: 12.50px; " x="57.860001" y="-2.8199999"></tspan> <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="8.3269978" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="19.867268" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="31.907656" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="41.634991" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="49.98" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="56.931667" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="61.095165" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="67.346664" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="72.547913" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="76.461357" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="84.100685" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="96.141075" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="100.30457" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,35.3,58.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,44.34,61.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="15.741277" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,67.03,58.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,73.74,61.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代pan> </text> <text transform="matrix(1,0,0,-1,77.9,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,88.09,61.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,109.46,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>。根据线性代数理论,<年代vg height="17.2875" id="M22" style="vertical-align:-3.13504pt;width:205.875px;" version="1.1" viewbox="0 0 205.875 17.2875" width="205.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.2875)"> <g transform="translate(72,-58.17)"> <text transform="matrix(1,0,0,-1,-71.95,61.35)"> <tspan style="font-size: 12.50px; " x="77.480003" y="-2.8199999"></tspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="14.866067" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="18.779507" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="22.943005" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.945404" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="44.985794" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.524864" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="61.252197" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="69.599998" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="76.551666" y="7.1054274e-015"> (</t年代pan> <tspan style="font-size: 12.50px; " x="80.715164" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="86.966667" y="7.1054274e-015"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="92.167915" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="96.081352" y="7.1054274e-015"> )</t年代pan> <tspan style="font-size: 12.50px; " x="100.24485" y="7.1054274e-015"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="110.25976" y="7.1054274e-015"> =</t年代pan> <tspan style="font-size: 12.50px; " x="122.30015" y="7.1054274e-015"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,56.63,58.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,61.5,61.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="16.266403" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="24.605904" y="0"> 吗?</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.95" id="M23" style="vertical-align:-3.2316pt;width:90.612503px;" version="1.1" viewbox="0 0 90.612503 14.95" width="90.612503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.95)"> <g transform="translate(72,-60.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <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> </text> <text transform="matrix(1,0,0,-1,-62.51,60.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.29,63.31)"> <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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="18.204369" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.244757" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="36.783825" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="40.947327" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="45.110825" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="49.024261" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="53.187763" y="0"> 吗?</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.3" id="M24" style="vertical-align:-1.29163pt;width:62.674999px;" version="1.1" viewbox="0 0 62.674999 12.3" width="62.674999" 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"> 1</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"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="29.119488" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="41.159878" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>。</gydF4y2Bap> <p><span class="statement" id="lem1"><span class="statement-title">引理1。</年代pan><i>考虑到非微扰系统</我><年代pan class="equation" id="EEq8"> <svg height="16.5375" id="M25" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" 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,-1,112.88,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.87569" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.0391889" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.952628" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.891792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.232014" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,146.1,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,157.52,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.8631871" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.0266862" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.891792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.232014" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.73,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,195.61,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.491697" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="45.723473" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="54.588097" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="59.451763" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="62.927601" y="0"> g</t年代pan> <tspan style="font-size: 12.50px; " x="69.1791" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="81.682098" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="85.845596" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="95.272858" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="99.436356" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="103.3498" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="107.5133" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="113.7523" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="278.51001" y="0.63"> (</t年代pan> <tspan style="font-size: 12.50px; " x="282.67349" y="0.63"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="288.92499" y="0.63"> )</t年代pan> </text> </g> </g> </svg></span><i>的收益<年代vg height="14.475" id="M26" style="vertical-align:-3.13504pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 14.475" width="11.1875" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.475" id="M27" style="vertical-align:-3.13504pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 14.475" width="11.1875" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.7375" id="M28" 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>都是正的常数。如果参数<年代vg height="14.6" id="M29" style="vertical-align:-3.13504pt;width:38.387501px;" version="1.1" viewbox="0 0 38.387501 14.6" width="38.387501" 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,-67.97,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,63.5)"> <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="14.6" id="M30" style="vertical-align:-3.13504pt;width:38.387501px;" version="1.1" viewbox="0 0 38.387501 14.6" width="38.387501" 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,-67.97,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,63.5)"> <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>选择满足条件的吗<年代vg height="19.0375" id="M31" style="vertical-align:-4.15945pt;width:54.112499px;" version="1.1" viewbox="0 0 54.112499 19.0375" width="54.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.0375)"> <g transform="translate(72,-56.77)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-67.97,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,60.96)"> <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,-43.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.25" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.49,60.96)"> <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"> 4</t年代pan> </text> </g> </g> </svg>,然后<年代vg height="13.45" id="M32" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M33" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> </text> </g> </g> </svg>渐近收敛于零在有限时间足够大的价值<年代vg height="10.7375" id="M34" 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>。</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>由于条件<年代vg height="19.0375" id="M35" style="vertical-align:-4.15945pt;width:54.112499px;" version="1.1" viewbox="0 0 54.112499 19.0375" width="54.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.0375)"> <g transform="translate(72,-56.77)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-67.97,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,60.96)"> <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,-43.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.25" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.49,60.96)"> <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"> 4</t年代pan> </text> </g> </g> </svg>,特征方程的根,<年代vg height="17.674999" id="M36" style="vertical-align:-3.13504pt;width:104.6px;" version="1.1" viewbox="0 0 104.6 17.674999" width="104.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.675)"> <g transform="translate(72,-57.86)"> <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,-66.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.8,61.03)"> <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,-43.48,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.6,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.2644835" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="19.617207" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-15,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.66,61.03)"> <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>,是真实的,独特的,消极的。现在为了简单起见,假设初始条件是<年代vg height="14.75" id="M37" style="vertical-align:-3.25793pt;width:57.900002px;" version="1.1" viewbox="0 0 57.900002 14.75" width="57.900002" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.53,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.66,63.5)"> <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>和<年代vg height="14.75" id="M38" style="vertical-align:-3.25793pt;width:57.900002px;" version="1.1" viewbox="0 0 57.900002 14.75" width="57.900002" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.53,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.66,63.5)"> <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>。因此,进入半平面轨迹<年代vg height="13.45" id="M39" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>(象限),如图<一个href="//www.newsama.com/journals/jcse/2012/564906/fig1/" target="_blank">1</一个>。当<年代vg height="13.45" id="M40" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>我们从(<一个href="#EEq8">8</一个>)获得<年代vg height="14.6" id="M41" style="vertical-align:-3.13504pt;width:169.53751px;" version="1.1" viewbox="0 0 169.53751 14.6" width="169.53751" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="15.803792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.144012" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-34.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="15.803792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.144012" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,8.28,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,13.15,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="23.055532" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="35.08342" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="43.647972" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>并知道其等价点<年代vg height="14.6" id="M42" style="vertical-align:-3.13504pt;width:114.1px;" version="1.1" viewbox="0 0 114.1 14.6" width="114.1" 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> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="23.255581" y="0"></tspan> <tspan style="font-size: 12.50px; " x="16.716511" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="24.043268" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="31.682602" 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="47.88649" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="56.451046" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="63.227673" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="66.703506" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,3.61,63.5)"> <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>。函数<年代vg height="13.6125" id="M43" style="vertical-align:-2.34499pt;width:23.112499px;" version="1.1" viewbox="0 0 23.112499 13.6125" width="23.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <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="6.1514759" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.314975" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="14.228414" y="0"> )</t年代pan> </text> </g> </g> </svg>是由<年代pan class="equation" id="eq9"> <svg height="33.424999" id="M44" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 33.424999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,33.425)"> <g transform="translate(72,-45.26)"> <text transform="matrix(1,0,0,-1,115.65,56.35)"> <tspan style="font-size: 12.50px; " x="114.77" y="-7.25"> ? ?</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="8.7270937" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.890593" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="16.804031" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.443365" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="43.022823" y="0"></tspan> <tspan style="font-size: 12.50px; " x="36.483753" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="45.898514" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="50.062012" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="53.975452" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="60.914616" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="72.267342" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="77.368561" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="86.783325" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="90.946823" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="94.86026" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="101.79942" y="0"> +</t年代pan> </text> <g> <path d="m 230,59.47 7.61,0" 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,-1,230,47.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.89" y="-8.7600002"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="15.753667" y="-8.7600002"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="19.229502" y="-8.7600002"> g</t年代pan> <tspan style="font-size: 12.50px; " x="25.481001" y="-8.7600002"> n</t年代pan> <tspan style="font-size: 12.50px; " x="37.984001" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="42.147499" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="51.57476" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="55.738262" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="59.651699" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="63.815201" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="70.054199" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="244.12" y="-7.9099998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="248.28349" y="-7.9099998"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="254.535" y="-7.9099998"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.475" id="M45" style="vertical-align:-3.13504pt;width:64.125px;" version="1.1" viewbox="0 0 64.125 14.475" width="64.125" 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> <tspan style="font-size: 12.50px; " x="10.389993" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.730213" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="30.307272" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="42.335159" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.63,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.475" id="M46" style="vertical-align:-3.13504pt;width:46.474998px;" version="1.1" viewbox="0 0 46.474998 14.475" width="46.474998" 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> <tspan style="font-size: 12.50px; " x="7.6018238" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="16.178883" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="28.219271" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.75,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>。的参数<年代vg height="13.55" id="M47" style="vertical-align:-2.29482pt;width:36.849998px;" version="1.1" viewbox="0 0 36.849998 13.55" width="36.849998" 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="11.077658" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="23.118048" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.0625" id="M48" style="vertical-align:-0.30096pt;width:33.700001px;" version="1.1" viewbox="0 0 33.700001 11.0625" width="33.700001" 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="8.5645552" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> 0</t年代pan> </text> </g> </g> </svg>是真正的常数。自<年代vg height="13.45" id="M49" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>,它是<年代vg height="14.6" id="M50" style="vertical-align:-3.13504pt;width:184.3px;" version="1.1" viewbox="0 0 184.3 14.6" width="184.3" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="15.803792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.144012" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-34.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="15.803792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.144012" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,8.28,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,13.15,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="22.355364" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="33.695583" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="43.948044" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="55.988434" y="0"> 0</t年代pan> </text> </g> </g> </svg>那<年代pan class="equation" id="eq10"> <svg height="140.64999" id="M51" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 140.64999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,140.65)"> <g transform="translate(72,40.52)"> <text transform="matrix(1,0,0,-1,83.05,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.391193" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="19.554691" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="23.46813" y="0"> )</t年代pan> </text> <g> <path d="m 83.05,56.57 27.63,0" 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,-1,91.59,44.69)"> <tspan style="font-size: 12.50px; " x="81.980003" y="-16.01"> ? ?</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="6.6515961" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="23.07" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="34.397717" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="42.012047" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="50.75164" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="54.915142" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="58.828579" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="66.467911" y="-8.7600002"> =</t年代pan> </text> <g> <path d="m 171.99,56.57 10.57,0" 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,-1,171.99,44.69)"> <tspan style="font-size: 12.50px; " x="13.85" y="-1.4299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="101.51" y="-16.01"> ? ?</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="6.6515961" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="29.77" y="-8.7600002"></tspan> <tspan style="font-size: 12.50px; " x="23.23093" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="32.645691" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="36.809189" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="40.72263" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="47.661793" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="59.002014" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="64.103241" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="73.530502" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="77.694" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="81.607437" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="88.5466" y="-8.7600002"> +</t年代pan> </text> <g> <path d="m 273.08,56.57 7.61,0" 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,-1,273.08,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8100004" y="-1.4299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-78.459999" y="38.299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="9.1999998" y="23.719999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-99.510002" y="30.969999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-88.169777" y="30.969999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-62.540001" y="30.969999"></tspan> <tspan style="font-size: 12.50px; " x="-69.079071" y="30.969999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-59.66431" y="30.969999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-55.500813" y="30.969999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-51.587372" y="30.969999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-44.648209" y="30.969999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-33.307987" y="30.969999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-28.206762" y="30.969999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-18.779499" y="30.969999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-14.616001" y="30.969999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-10.702562" y="30.969999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-3.763397" y="30.969999"> +</t年代pan> </text> <g> <path d="m 281.86,16.85 7.61,0" 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,-1,281.86,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8100004" y="-1.42"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-123.8" y="21.219999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-104.52037" y="21.219999"></tspan> <tspan style="font-size: 12.50px; " x="-111.05944" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-101.64468" y="21.219999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-97.481186" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-93.567749" y="21.219999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-86.628578" y="21.219999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-75.288361" y="21.219999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-71.124863" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-60.734867" y="21.219999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-49.382145" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-44.280918" y="21.219999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-31.490351" y="21.219999"></tspan> <tspan style="font-size: 12.50px; " x="-38.029419" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-28.61466" y="21.219999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-24.451162" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-20.537724" y="21.219999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-13.598558" y="21.219999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-2.258337" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="5.3559899" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.457214" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="19.884476" y="21.219999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="24.047976" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="27.961414" y="21.219999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="34.900578" y="21.219999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="46.253304" y="21.219999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-123.8" y="41.689999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-104.52037" y="41.689999"></tspan> <tspan style="font-size: 12.50px; " x="-111.05944" y="41.689999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-101.64468" y="41.689999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-97.481186" y="41.689999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-93.567749" y="41.689999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-86.628578" y="41.689999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-75.288361" y="41.689999"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,210.56,-39.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,221.98,-36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.8631871" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.0266862" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.891792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.232014" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,255.19,-39.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,260.07,-36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.491697" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.430862" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.771084" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="46.023544" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="58.063931" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="64.31543" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="207.8" y="-49.330002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="211.9635" y="-49.330002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="218.215" y="-49.330002"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="224.46649" y="-49.330002"> )</t年代pan> </text> </g> </g> </svg></span>因此,我们可以获得<年代vg height="15.5" id="M52" style="vertical-align:-2.34499pt;width:93.574997px;" version="1.1" viewbox="0 0 93.574997 15.5" width="93.574997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.5)"> <g transform="translate(72,-59.6)"> <text transform="matrix(1,0,0,-1,-71.95,61.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.314975" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="14.228414" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="21.855244" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="33.895634" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="40.047108" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="44.210609" y="0"> 0</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="54.625607" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-11.75,66.99)"> <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="11.316336" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>。它遵循的上界<年代vg height="13.6125" id="M53" style="vertical-align:-2.34499pt;width:23.112499px;" version="1.1" viewbox="0 0 23.112499 13.6125" width="23.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <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="6.1514759" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.314975" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="14.228414" y="0"> )</t年代pan> </text> </g> </g> </svg>是<年代vg height="15.5" id="M54" style="vertical-align:-2.34499pt;width:84.400002px;" version="1.1" viewbox="0 0 84.400002 15.5" width="84.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.5)"> <g transform="translate(72,-59.6)"> <text transform="matrix(1,0,0,-1,-71.95,61.99)"> <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="8.6520758" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.815575" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="16.729013" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="20.892513" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="26.856443" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="38.896832" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="47.286346" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-19.09,66.99)"> <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="11.316336" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>在哪里<年代vg height="11.0625" id="M55" style="vertical-align:-0.30096pt;width:37.8125px;" version="1.1" viewbox="0 0 37.8125 11.0625" width="37.8125" 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="11.852844" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="23.893232" y="0"> 0</t年代pan> </text> </g> </g> </svg>是一个常数。选择一个李雅普诺夫函数<年代vg height="16.5375" id="M56" style="vertical-align:-2.21957pt;width:104.75px;" version="1.1" viewbox="0 0 104.75 16.5375" width="104.75" 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="7.1892252" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.352724" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.266163" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="22.892994" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="34.93338" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="39.096882" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="45.348381" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="48.824215" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="55.075714" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="59.239216" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.49,61.03)"> <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="8.0769377" y="0"> )</t年代pan> </text> </g> </g> </svg>然后得到它的时间导数<年代pan class="equation" id="eq11"> <svg height="83.087502" id="M57" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 83.087502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,83.0875)"> <g transform="translate(72,-5.53)"> <text transform="matrix(1,0,0,-1,71.7,55.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="117.32" y="9.8599997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="163.41" y="-4.7199998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-7.8800001" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="4.1978979" y="2.53"> (</t年代pan> <tspan style="font-size: 12.50px; " x="8.3613968" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="12.274836" y="2.53"> )</t年代pan> <tspan style="font-size: 12.50px; " x="19.914169" y="2.53"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.642223" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="42.069485" y="2.53"> (</t年代pan> <tspan style="font-size: 12.50px; " x="46.232983" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="50.146423" y="2.53"> )</t年代pan> <tspan style="font-size: 12.50px; " x="62.936993" y="2.53"></tspan> <tspan style="font-size: 12.50px; " x="56.397923" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="65.812683" y="2.53"> (</t年代pan> <tspan style="font-size: 12.50px; " x="69.976181" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="73.889618" y="2.53"> )</t年代pan> <tspan style="font-size: 12.50px; " x="81.528954" y="2.53"> =</t年代pan> <tspan style="font-size: 12.50px; " x="93.569344" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="102.9841" y="2.53"> (</t年代pan> <tspan style="font-size: 12.50px; " x="107.1476" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="111.06104" y="2.53"> )</t年代pan> <tspan style="font-size: 12.50px; " x="126.7" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="135.42709" y="2.53"> (</t年代pan> <tspan style="font-size: 12.50px; " x="139.59059" y="2.53"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="143.50403" y="2.53"> )</t年代pan> <tspan style="font-size: 12.50px; " x="150.44319" y="2.53"> - - - - - -</t年代pan> </text> <g> <path d="m 234.69,56.57 7.61,0" 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,-1,234.69,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="108.87" y="-1.4299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-118.87" y="26.48"> |</t年代pan> <tspan style="font-size: 12.50px; " x="-118.87" y="29.639999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="-94.699997" y="26.48"> |</t年代pan> <tspan style="font-size: 12.50px; " x="-94.699997" y="29.639999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="-90.120003" y="28.07"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.89" y="-8.7600002"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="15.753667" y="-8.7600002"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="19.229502" y="-8.7600002"> g</t年代pan> <tspan style="font-size: 12.50px; " x="25.481001" y="-8.7600002"> n</t年代pan> <tspan style="font-size: 12.50px; " x="37.984001" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="42.147499" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="51.57476" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="55.738262" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="59.651699" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="63.815201" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="70.754364" y="-8.7600002"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="82.094582" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="87.195808" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="96.62307" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="100.78657" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="104.70001" y="-8.7600002"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-146.55" y="28.07"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-130.34612" y="28.07"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-116.37" y="28.07"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-106.94274" y="28.07"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-102.77924" y="28.07"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-98.865799" y="28.07"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.14,21.62)"> <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="11.316336" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,167.48,16.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="12.96" y="-7.25"> ? ?</t年代pan> </text> <g> <path d="m 180.02,19.75 7.61,0" 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,-1,180.02,7.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.89" y="-10.34"> |</t年代pan> <tspan style="font-size: 12.50px; " x="10.89" y="-7.1799998"> |</t年代pan> <tspan style="font-size: 12.50px; " x="35.049999" y="-10.34"> |</t年代pan> <tspan style="font-size: 12.50px; " x="35.049999" y="-7.1799998"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.39" y="-8.75"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="22.804758" y="-8.75"> (</t年代pan> <tspan style="font-size: 12.50px; " x="26.968258" y="-8.75"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="30.881697" y="-8.75"> )</t年代pan> <tspan style="font-size: 12.50px; " x="40.330002" y="-8.75"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="51.670219" y="-8.75"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="56.771446" y="-8.75"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,244.14,21.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,251.1,16.63)"> <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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="216.77" y="-19.01"> (</t年代pan> <tspan style="font-size: 12.50px; " x="220.9335" y="-19.01"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="227.185" y="-19.01"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="233.43649" y="-19.01"> )</t年代pan> </text> </g> </g> </svg></span>自<年代vg height="13.55" id="M58" style="vertical-align:-2.29482pt;width:36.849998px;" version="1.1" viewbox="0 0 36.849998 13.55" width="36.849998" 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="11.077658" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="23.118048" y="0"> 0</t年代pan> </text> </g> </g> </svg>存在一个有限的时间,<年代vg height="14.6" id="M59" style="vertical-align:-3.13504pt;width:42.012501px;" version="1.1" viewbox="0 0 42.012501 14.6" width="42.012501" 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,-65.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.73,63.5)"> <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>,这样<年代vg height="15.4375" id="M60" style="vertical-align:-2.29482pt;width:113.4px;" version="1.1" viewbox="0 0 113.4 15.4375" width="113.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4375)"> <g transform="translate(72,-59.65)"> <text transform="matrix(1,0,0,-1,-71.95,61.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.389513" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58,66.99)"> <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="11.325088" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.96,61.99)"> <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="22.968012" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="26.443846" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="34.05817" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="40.997337" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="52.35006" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>为一个足够大的收获<年代vg height="10.7375" id="M61" 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>和<年代vg height="14.2375" id="M62" style="vertical-align:-3.13504pt;width:39.087502px;" version="1.1" viewbox="0 0 39.087502 14.2375" width="39.087502" 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> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-45.65,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="13.55" id="M63" style="vertical-align:-2.29482pt;width:35.174999px;" version="1.1" viewbox="0 0 35.174999 13.55" width="35.174999" 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="9.7398367" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> 0</t年代pan> </text> </g> </g> </svg>是一个常数。因此,<年代pan class="equation" id="eq12"> <svg height="18.512501" id="M64" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.512501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5125)"> <g transform="translate(72,-57.19)"> <text transform="matrix(1,0,0,-1,85.25,63.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="54.439999" y="0.94999999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="54.439999" y="4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="78.599998" y="0.94999999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="78.599998" y="4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="-7.8800001" y="2.54"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="4.1978979" y="2.54"> (</t年代pan> <tspan style="font-size: 12.50px; " x="8.3613968" y="2.54"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="12.274836" y="2.54"> )</t年代pan> <tspan style="font-size: 12.50px; " x="19.914169" y="2.54"> =</t年代pan> <tspan style="font-size: 12.50px; " x="34.730225" y="2.54"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="46.070446" y="2.54"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="56.939999" y="2.54"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="66.354759" y="2.54"> (</t年代pan> <tspan style="font-size: 12.50px; " x="70.518257" y="2.54"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="74.431694" y="2.54"> )</t年代pan> <tspan style="font-size: 12.50px; " x="83.879997" y="2.54"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="95.220222" y="2.54"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="100.32144" y="2.54"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.92,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,199.87,61.04)"> <tspan style="font-size: 12.50px; " x="50.240002" y="-1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="50.240002" y="1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="74.400002" y="-1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="74.400002" y="1.58"> |</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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="15.716271" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.532326" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="41.872547" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="52.740002" y="0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="62.154758" y="0.0099999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="66.31826" y="0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="70.231697" y="0.0099999998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="88.949997" y="0.0099999998"> f</t年代pan> <tspan style="font-size: 12.50px; " x="92.713402" y="0.0099999998"> o</t年代pan> <tspan style="font-size: 12.50px; " x="98.964905" y="0.0099999998"> r</t年代pan> <tspan style="font-size: 12.50px; " x="107.2919" y="0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="114.68118" y="0.0099999998"> ></t年代pan> <tspan style="font-size: 12.50px; " x="126.70906" y="0.0099999998"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,333.47,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,338.34,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="129.53" y="-0.44"> (</t年代pan> <tspan style="font-size: 12.50px; " x="133.6935" y="-0.44"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="139.94499" y="-0.44"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="146.1965" y="-0.44"> )</t年代pan> </text> </g> </g> </svg></span>上面的方程意味着函数<年代vg height="13.45" id="M65" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" y="0"> )</t年代pan> </text> </g> </g> </svg>在有限时间内收敛到零。让的轨迹(<一个href="#EEq8">8</一个>下次)相交轴<年代vg height="13.45" id="M66" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>在点<年代vg height="14.6" id="M67" style="vertical-align:-3.13504pt;width:30.6875px;" version="1.1" viewbox="0 0 30.6875 14.6" width="30.6875" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.53,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.66,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>。从特征方程的根,<年代vg height="17.674999" id="M68" style="vertical-align:-3.13504pt;width:104.6px;" version="1.1" viewbox="0 0 104.6 17.674999" width="104.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.675)"> <g transform="translate(72,-57.86)"> <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,-66.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.8,61.03)"> <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,-43.48,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.6,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.2644835" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="19.617207" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-15,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.66,61.03)"> <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>,是稳定的,我们知道螺旋轨迹收敛的等价点和行为<年代vg height="13.45" id="M69" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> </text> </g> </g> </svg>单调变化。因此,<年代pan class="equation" id="eq13"> <svg height="45.787498" id="M70" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.787498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.7875)"> <g transform="translate(72,-35.37)"> <text transform="matrix(1,0,0,-1,168.9,62.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1800001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="11.92" y="4.1100001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="17.77" y="1.6"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.04" y="1.6"></tspan> <tspan style="font-size: 12.50px; " x="2.500931" y="1.6"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.59,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,195.46,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-0.93000001"> |</t年代pan> </text> <g> <path d="m 168.9,53.68 34.91,0" 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,-1,168.9,41.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1900001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="11.92" y="4.1100001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="17.77" y="1.6"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.04" y="1.6"></tspan> <tspan style="font-size: 12.50px; " x="2.500931" y="1.6"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.59,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,195.46,37.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-0.92000002"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.02" y="-13.09"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.047886" y="-13.09"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="34.250095" y="-13.09"> <</t年代pan> <tspan style="font-size: 12.50px; " x="46.290482" y="-13.09"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="52.541985" y="-13.09"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="272.41" y="-13.09"> (</t年代pan> <tspan style="font-size: 12.50px; " x="276.57349" y="-13.09"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="282.82501" y="-13.09"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="289.07651" y="-13.09"> )</t年代pan> </text> </g> </g> </svg></span>扩展到半平面轨迹<年代vg height="13.45" id="M71" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>类似的推理实现后连续穿过轴<年代vg height="13.45" id="M72" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>满足不等式<年代vg height="15.05" id="M73" style="vertical-align:-3.49493pt;width:140.6875px;" version="1.1" viewbox="0 0 140.6875 15.05" width="140.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.05)"> <g transform="translate(72,-59.96)"> <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="9.039669" y="0"></tspan> <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="13.990857" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.03,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.44,63.5)"> <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="6.6640992" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="10.139933" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="19.179602" y="0"></tspan> <tspan style="font-size: 12.50px; " x="12.640533" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-12.38,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-9.16,63.5)"> <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="10.12743" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="31.357525" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="43.397915" y="0"> 1</t年代pan> </text> </g> </g> </svg>。因此,解决交叉轴<年代vg height="13.45" id="M74" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>从象限二象限的我,从第四象限第三象限。系统的每一个轨迹穿过轴<年代vg height="13.45" id="M75" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>在有限的时间。之后将这些路径<年代vg height="13.45" id="M76" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>,得到系统的相图,如图<一个href="//www.newsama.com/journals/jcse/2012/564906/fig1/" target="_blank">1</一个>。该算法的特点是扭曲的相图在起源和无限环绕原点。根据黎凡特的论文(<一个href="#B14">14</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B16">16</一个>),总收敛时间估计<年代pan class="equation" id="eq14"> <svg height="40.662498" id="M77" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.6625)"> <g transform="translate(72,-39.47)"> <text transform="matrix(1,0,0,-1,70.76,50.56)"> <tspan style="font-size: 12.50px; " x="24.469999" y="6.5500002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="42.709999" y="-1.59"> |</t年代pan> <tspan style="font-size: 12.50px; " x="42.709999" y="1.59"> |</t年代pan> <tspan style="font-size: 12.50px; " x="54.630001" y="2.52"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="60.48" y="-7.1054274e-015"> ? ?</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="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="51.759998" y="-7.1054274e-015"></tspan> <tspan style="font-size: 12.50px; " x="45.220932" y="-7.1054274e-015"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,135.16,47.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,138.38,48.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-0.93000001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="11.82" y="-2.52"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.950001" y="-4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="25.950001" y="-0.93000001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="37.869999" y="-7.1054274e-015"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="43.720001" y="-2.52"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="34.990002" y="-2.52"></tspan> <tspan style="font-size: 12.50px; " x="28.450932" y="-2.52"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,186.01,47.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.89,48.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-0.93000001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="10.43" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="16.290001" y="-2.52"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.304663" y="-2.52"> +</t年代pan> <tspan style="font-size: 12.50px; " x="36.657387" y="-2.52"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="45.159428" y="-2.52"> +</t年代pan> <tspan style="font-size: 12.50px; " x="56.499649" y="-2.52"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,253.62,55.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.28,50.56)"> <tspan style="font-size: 12.50px; " x="25" y="2.52"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="34.330002" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="47.560001" y="-12.17"> |</t年代pan> <tspan style="font-size: 12.50px; " x="47.560001" y="-8.9899998"> |</t年代pan> <tspan style="font-size: 12.50px; " x="59.48" y="-8.0600004"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="65.330002" y="-10.57"> ? ?</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="11.327718" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="56.599998" y="-10.57"></tspan> <tspan style="font-size: 12.50px; " x="50.060932" y="-10.57"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,330.53,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,335.4,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-0.93000001"> |</t年代pan> </text> <g> <path d="m 308.84,53.68 34.91,0" 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,-1,313,41.81)"> <tspan style="font-size: 12.50px; " x="31.950001" y="-8.75"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</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="20.367388" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="154.87" y="-10.8"> (</t年代pan> <tspan style="font-size: 12.50px; " x="159.03349" y="-10.8"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="165.285" y="-10.8"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="171.5365" y="-10.8"> )</t年代pan> </text> </g> </g> </svg></span>因此,我们表明,该轨迹可以执行旋转原点在有限时间收敛到原点的相平面。有限时间收敛到原点是由于切换两种不同控制振幅随着轨迹接近原点(<一个href="#B18">18</一个>]。这个定理的证明是完成了。</年代pan></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="564906.fig.001" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.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/2012/564906/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 阶段修改后的二阶滑模系统的路径。</t一个ble> </div> </div> </div> <p><span class="statement" id="lem2"><span class="statement-title">引理2。</年代pan><i>考虑以下系统:</我><年代pan class="equation" id="EEq9"> <svg height="16.5375" id="M78" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" 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,-1,94.44,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.8631871" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.0266862" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.891792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.232014" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,127.65,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,139.07,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.87569" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.0391889" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.952628" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.891792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.232014" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,172.29,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,177.16,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.491697" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="37.171417" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="45.735973" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="54.600601" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="59.464268" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="62.940102" y="0"> g</t年代pan> <tspan style="font-size: 12.50px; " x="69.191605" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="81.694603" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="85.858101" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="95.272858" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="99.436356" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="103.3498" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="107.5133" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="114.46497" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="125.80518" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="136.32021" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="140.4837" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="144.39714" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="150.64865" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="290.70999" y="0.63"> (</t年代pan> <tspan style="font-size: 12.50px; " x="294.8735" y="0.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="301.125" y="0.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="307.3765" y="0.63"> )</t年代pan> </text> </g> </g> </svg></span><i>的函数<年代vg height="13.6125" id="M79" style="vertical-align:-2.34499pt;width:24.1px;" version="1.1" viewbox="0 0 24.1 13.6125" width="24.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <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="6.9391651" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.016103" y="0"> )</t年代pan> </text> </g> </g> </svg>有上界<年代vg height="13.6125" id="M80" style="vertical-align:-2.34499pt;width:57.549999px;" version="1.1" viewbox="0 0 57.549999 13.6125" width="57.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <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="2.5006001" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.439765" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.603264" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.516703" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="21.680202" 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="39.684521" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.55" id="M81" 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>是一个已知的常数。如果参数<年代vg height="14.6" id="M82" style="vertical-align:-3.13504pt;width:38.387501px;" version="1.1" viewbox="0 0 38.387501 14.6" width="38.387501" 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,-67.97,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,63.5)"> <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="14.6" id="M83" style="vertical-align:-3.13504pt;width:38.387501px;" version="1.1" viewbox="0 0 38.387501 14.6" width="38.387501" 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,-67.97,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,63.5)"> <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>,获得<年代vg height="10.7375" id="M84" 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>选择满足下列条件:</我><年代pan class="equation" id="EEq10"> <svg height="37.5" id="M85" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.5" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.5)"> <g transform="translate(72,-42)"> <text transform="matrix(1,0,0,-1,163.09,50.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,167.07,47.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.41,50.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.16"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.87,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.25" y="9.21"> 1</t年代pan> </text> <g> <path d="m 188.65,53.93 9.1,0" 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,-1,190.07,42.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="8.8699999" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="34.00103" y="-8.75"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="44.25349" y="-8.75"> ></t年代pan> <tspan style="font-size: 12.50px; " x="56.29388" y="-8.75"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="62.54538" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="277.79999" y="-11.82"> (</t年代pan> <tspan style="font-size: 12.50px; " x="281.9635" y="-11.82"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="288.215" y="-11.82"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="294.46649" y="-11.82"> )</t年代pan> </text> </g> </g> </svg></span><i>然后<年代vg height="13.45" id="M86" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M87" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> </text> </g> </g> </svg>在有限时间内收敛到零。</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>我们的参数<年代vg height="14.475" id="M88" style="vertical-align:-3.13504pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 14.475" width="11.1875" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.475" id="M89" style="vertical-align:-3.13504pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 14.475" width="11.1875" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>满足条件<年代vg height="19.0375" id="M90" style="vertical-align:-4.15945pt;width:54.112499px;" version="1.1" viewbox="0 0 54.112499 19.0375" width="54.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.0375)"> <g transform="translate(72,-56.77)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-67.97,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,60.96)"> <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,-43.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.25" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.49,60.96)"> <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"> 4</t年代pan> </text> </g> </g> </svg>然后获得系统的特征多项式(<一个href="#EEq9">15</一个>)有两种截然不同的现实根源<年代vg height="16.012501" id="M91" style="vertical-align:-4.37273pt;width:87.724998px;" version="1.1" viewbox="0 0 87.724998 16.012501" width="87.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.0125)"> <g transform="translate(72,-59.19)"> <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"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.27,63.6)"> <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> <tspan style="font-size: 12.50px; " x="20.592442" 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="32.857883" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="41.42244" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="11.0625" id="M92" style="vertical-align:-0.30096pt;width:36.137501px;" version="1.1" viewbox="0 0 36.137501 11.0625" width="36.137501" 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="10.515023" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.55" id="M93" 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="13.425" id="M94" style="vertical-align:-2.29482pt;width:37.049999px;" version="1.1" viewbox="0 0 37.049999 13.425" width="37.049999" 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="10.440005" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.480394" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.475" id="M95" style="vertical-align:-3.13504pt;width:65.762497px;" version="1.1" viewbox="0 0 65.762497 14.475" width="65.762497" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,63.6)"> <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="21.867746" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="33.20797" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.475" id="M96" style="vertical-align:-3.13504pt;width:48.112499px;" version="1.1" viewbox="0 0 48.112499 14.475" width="48.112499" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.63,63.6)"> <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="19.092081" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>。当条件<年代vg height="13.45" id="M97" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>,(<一个href="#EEq9">15</一个>)成为<年代pan class="equation" id="eq17"> <svg height="16.5375" id="M98" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" 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,-1,124.02,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.87569" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.0391889" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.952628" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.891792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.232014" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,157.24,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,168.66,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.8631871" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.0266862" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.891792" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.232014" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,201.87,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.75,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.491697" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="37.171417" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="45.735973" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="55.288265" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="66.628487" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="77.156013" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="81.319511" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="85.232948" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="91.471947" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="261.12" y="0.63"> (</t年代pan> <tspan style="font-size: 12.50px; " x="265.28351" y="0.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="271.535" y="0.63"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="277.7865" y="0.63"> )</t年代pan> </text> </g> </g> </svg></span>让<年代vg height="14.6" id="M99" style="vertical-align:-3.13504pt;width:99.837502px;" version="1.1" viewbox="0 0 99.837502 14.6" width="99.837502" 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,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.28,63.5)"> <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="22.155315" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="33.495537" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="44.435661" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="47.911495" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.39,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.51,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.875" id="M100" style="vertical-align:-3.13504pt;width:76.074997px;" version="1.1" viewbox="0 0 76.074997 13.875" width="76.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.875)"> <g transform="translate(72,-60.9)"> <text transform="matrix(1,0,0,-1,-71.95,64.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.28,64.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.08" y="-0.1"></tspan> <tspan style="font-size: 12.50px; " x="12.04" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.91,60.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.56,64.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"></tspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>。由此可见,<年代pan class="equation" id="eq18"> <svg height="62.637501" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 62.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,62.6375)"> <g transform="translate(72,-21.89)"> <text transform="matrix(1,0,0,-1,80.98,43.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="29.610001" y="-12.94"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="29.610001" y="-2.0899999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="29.610001" y="8.75"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="29.610001" y="19.540001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-6.4699998" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="1.856998" y="0.14"> (</t年代pan> <tspan style="font-size: 12.50px; " x="6.0204968" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.9339361" y="0.14"> )</t年代pan> <tspan style="font-size: 12.50px; " x="17.573269" y="0.14"> =</t年代pan> <tspan style="font-size: 12.50px; " x="40.82" y="-10.49"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="64.213112" y="-10.49"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="35.240002" y="14.52"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="43.804554" y="14.52"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,128.76,26.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,139.61,29.44)"> <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,-1,152.15,26.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,157.03,56.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.85"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.690001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="32.48"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="10.85"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="21.690001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="32.48"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="13.33" y="2.45"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.69,51.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.65,54.45)"> <tspan style="font-size: 12.50px; " x="-13.29" y="25.01"> ? ?</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="8.0769377" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.69,26.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.65,29.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="-27.450001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="-16.6"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="-5.7600002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="5.0300002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="20.639999" y="-14.37"> +</t年代pan> <tspan style="font-size: 12.50px; " x="31.99" y="-27.450001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="31.99" y="-16.6"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="31.99" y="-5.7600002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="31.99" y="5.0300002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.869999" y="-25"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="60.380001" y="-27.450001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="60.380001" y="-16.6"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="60.380001" y="-5.7600002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="60.380001" y="5.0300002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="37.610001" y="0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="48.125023" y="0.0099999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="52.288521" y="0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="56.201962" y="0.0099999998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="69.480003" y="-14.37"> =</t年代pan> <tspan style="font-size: 12.50px; " x="81.507889" y="-14.37"> F</t年代pan> <tspan style="font-size: 12.50px; " x="91.047676" y="-14.37"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="99.387177" y="-14.37"> (</t年代pan> <tspan style="font-size: 12.50px; " x="103.55067" y="-14.37"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="107.46411" y="-14.37"> )</t年代pan> <tspan style="font-size: 12.50px; " x="114.40328" y="-14.37"> +</t年代pan> <tspan style="font-size: 12.50px; " x="125.7435" y="-14.37"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="132.69518" y="-14.37"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="143.22269" y="-14.37"> (</t年代pan> <tspan style="font-size: 12.50px; " x="147.3862" y="-14.37"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="151.29964" y="-14.37"> )</t年代pan> <tspan style="font-size: 12.50px; " x="157.55113" y="-14.37"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="284.22" y="-14.37"> (</t年代pan> <tspan style="font-size: 12.50px; " x="288.38348" y="-14.37"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="294.63501" y="-14.37"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="300.88651" y="-14.37"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代pan class="equation" id="eq19"> <svg height="62.637501" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 62.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,62.6375)"> <g transform="translate(72,-21.89)"> <text transform="matrix(1,0,0,-1,71.23,43.82)"> <tspan style="font-size: 12.50px; " x="21.76" y="4.9200001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="27.5" y="1.88"> ? ?</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="9.7148314" y="0"> =</t年代pan> </text> <text transform="matrix(1,0,0,-1,105.06,46.94)"> <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"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,117.75,41.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,124.08,46.94)"> <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"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,130.79,38.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> </text> <text transform="matrix(1,0,0,-1,136.53,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,146.71,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> R</t年代pan> </text> <text transform="matrix(1,0,0,-1,168.09,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,172.96,43.82)"> <tspan style="font-size: 12.50px; " x="50.189999" y="-13.08"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="50.189999" y="-2.23"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="50.189999" y="8.6099997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="50.189999" y="19.4"> 吗?</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="25.131029" y="0"> F</t年代pan> <tspan style="font-size: 12.50px; " x="38.146652" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="61.400002" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="84.780609" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="55.82" y="14.38"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="64.384552" y="14.38"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,241.32,26.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,252.17,29.44)"> <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,-1,264.71,26.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,269.58,56.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.85"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.690001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="32.48"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="55.310001" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="55.310001" y="10.85"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="55.310001" y="21.690001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="55.310001" y="32.48"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="60.939999" y="2.45"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="60.939999" y="27.459999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="67.190002" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="67.190002" y="10.85"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="67.190002" y="21.690001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="67.190002" y="32.48"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="13.08"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="32.84103" y="13.08"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="43.268532" y="13.08"> =</t年代pan> <tspan style="font-size: 12.50px; " x="74.900002" y="13.08"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="198.28999" y="13.08"> (</t年代pan> <tspan style="font-size: 12.50px; " x="202.45351" y="13.08"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="208.705" y="13.08"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="214.9565" y="13.08"> )</t年代pan> </text> </g> </g> </svg></span>写上述动力学方程显式形式作为其解决方案<年代pan class="equation" id="eq20"> <svg height="87.862503" id="M103" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 87.862503" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,87.8625)"> <g transform="translate(72,-1.71)"> <text transform="matrix(1,0,0,-1,114.52,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="16.403936" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.043268" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="36.783825" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,156.86,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> F</t年代pan> <tspan style="font-size: 8.75px; " x="6.6777759" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,166.77,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="25.693665" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="37.033886" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,209.36,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> F</t年代pan> <tspan style="font-size: 8.75px; " x="6.6777759" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,221.36,45.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> </text> <text transform="matrix(1,0,0,-1,228.36,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,234.07,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.62,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> F</t年代pan> <tspan style="font-size: 8.75px; " x="6.6777759" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,251.28,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.46669" 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="28.031727" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="34.283226" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="40.934822" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-112.71" y="39.580002"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-99.981949" y="39.580002"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,156.86,18.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> F</t年代pan> <tspan style="font-size: 8.75px; " x="6.6777759" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,166.77,13.38)"> <tspan style="font-size: 12.50px; " x="37.040001" y="7.6900001"> 吗?</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="8.3269978" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="25.693665" y="0"> +</t年代pan> </text> <text transform="matrix(1,0,0,-1,210.81,27.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,216.52,13.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,222.07,18.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> F</t年代pan> <tspan style="font-size: 8.75px; " x="6.6777759" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,233.73,13.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.46669" 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="28.319296" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="39.659515" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="46.06105" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="52.312553" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="58.964149" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="65.365685" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="234.14" y="-20.35"> (</t年代pan> <tspan style="font-size: 12.50px; " x="238.3035" y="-20.35"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="244.55499" y="-20.35"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="250.8065" y="-20.35"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代pan class="equation" id="eq21"> <svg height="71.487503" id="M104" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 71.487503" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,71.4875)"> <g transform="translate(72,-14.81)"> <text transform="matrix(1,0,0,-1,70.82,40.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,76.37,45.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> F</t年代pan> <tspan style="font-size: 8.75px; " x="6.6777759" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,89.76,40.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-16.610001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-6.71"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="3.1900001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="13.09"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="22.93"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="29.809999" y="-21.42"> 1</t年代pan> </text> <g> <path d="m 108.62,57.57 28.15,0" 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,-1,108.62,45.69)"> <tspan style="font-size: 12.50px; " x="31.43" y="-6.2399998"> 吗?</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="9.7398367" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.092562" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="37.279999" y="-8.7600002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="44.244171" y="-8.7600002"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,158.44,59.45)"> <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"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.39,54.45)"> <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="18.37941" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,199.34,59.45)"> <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"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="10.878736" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,213.46,51.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="30.99" y="-9.7700005"> 1</t年代pan> </text> <g> <path d="m 233.5,57.57 28.15,0" 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,-1,233.5,45.69)"> <tspan style="font-size: 12.50px; " x="31.43" y="-6.2399998"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="37.279999" y="-8.7600002"> ? ?</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="9.7523403" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.092562" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,276.34,59.45)"> <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"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="10.931248" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,293.29,54.45)"> <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,-1,310.2,59.45)"> <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"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="10.869984" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,324.32,51.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-201.63" y="17.73"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-194.57831" y="17.73"> ? ?</t年代pan> </text> <g> <path d="m 115.63,29.03 28.15,0" 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,-1,115.63,17.15)"> <tspan style="font-size: 12.50px; " x="31.43" y="-6.2399998"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="37.279999" y="-8.75"> ? ?</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="9.8273582" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.16758" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,158.48,30.9)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.42,25.9)"> <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,-1,192.33,30.9)"> <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="10.878736" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.45,23.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="30.99" y="-9.7600002"> 1</t年代pan> </text> <g> <path d="m 226.49,29.03 28.15,0" 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,-1,226.49,17.15)"> <tspan style="font-size: 12.50px; " x="31.43" y="-6.2399998"> 吗?</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="9.8148546" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.16758" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="37.279999" y="-8.75"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="44.319187" y="-8.75"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,276.38,30.9)"> <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="10.931248" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,293.33,25.9)"> <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="18.316895" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,317.21,30.9)"> <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="10.878736" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,331.33,23.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-33.5"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-23.6"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-13.7"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-3.8"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="6.04"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="13.56" y="-16.889999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="136.53999" y="-16.889999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="140.70351" y="-16.889999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="146.955" y="-16.889999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="153.2065" y="-16.889999"> )</t年代pan> </text> </g> </g> </svg></span>的上界<年代vg height="14.6" id="M105" style="vertical-align:-3.13504pt;width:29.424999px;" version="1.1" viewbox="0 0 29.424999 14.6" width="29.424999" 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,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.75,63.5)"> <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="8.0769377" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M106" style="vertical-align:-3.13504pt;width:29.424999px;" version="1.1" viewbox="0 0 29.424999 14.6" width="29.424999" 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,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.75,63.5)"> <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="8.0769377" y="0"> )</t年代pan> </text> </g> </g> </svg>可以构造成<年代pan class="equation" id="eq22"> <svg height="510.03751" id="M107" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 510.03751" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,510.0375)"> <g transform="translate(72,336.03)"> <text transform="matrix(1,0,0,-1,55.83,54.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,64.65,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,71.61,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="-1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="1.59"> |</t年代pan> <tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.0834389" y="0.0099999998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.219999" y="0.0099999998"> =</t年代pan> <tspan style="font-size: 12.50px; " x="34.411385" y="0.0099999998"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,114.42,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,119.3,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,124.86,57.96)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,141.81,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="23.48" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 154.35,56.09 28.15,0" 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,-1,154.35,44.21)"> <tspan style="font-size: 12.50px; " x="31.42" y="-1.05"> 吗?</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="9.7398367" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.092562" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.78,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,198.48,54.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.23"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.62"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.55,57.96)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,225.24,52.96)"> <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,-1,242.14,57.96)"> <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="10.878736" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,258,54.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.23"> |</t年代pan> <tspan style="font-size: 12.50px; " x="4.5900002" y="0.029999999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="4.5900002" y="3.2"> |</t年代pan> <tspan 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x="-45.540001" y="24.780001"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="-32.68" y="32.110001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-23.299999" y="32.48"> 吗?</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="9.7398367" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.092562" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,138.05,-158.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 8</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,148.74,-171.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.23"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.62"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.551692" y="1.62"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,163.86,-167.86)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,182.55,-172.86)"> <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="18.37941" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.5,-167.86)"> <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="10.878736" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,225.14,-172.86)"> <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="15.50372" y="0"> ? ?</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="36.671299" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="43.647972" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="49.899471" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.61,-167.86)"> <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="10.869984" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,296.47,-171.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.23"> |</t年代pan> <tspan style="font-size: 12.50px; " x="17.629999" y="8.9499998"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="4.5799999" y="1.62"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="11.231596" y="1.62"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-203.17" y="36.66"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-190.44194" y="36.66"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,114.42,-211.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,119.3,-207.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,124.86,-202.89)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,141.81,-207.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="23.48" y="-8.3100004"> ? ?</t年代pan> </text> <g> <path d="m 154.35,-204.77 28.15,0" 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,-1,154.35,-216.65)"> <tspan style="font-size: 12.50px; " x="-45.540001" y="29.76"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="-32.68" y="37.080002"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-23.299999" y="37.450001"> 吗?</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="9.7398367" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.092562" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,138.05,-232.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 8</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,148.74,-248.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</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="12.901692" y="-2.51"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,167.21,-241.41)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,185.9,-246.41)"> <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="18.37941" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,209.85,-241.41)"> <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="10.878736" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,225.71,-248.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="73.669998" y="5.1799998"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="14.591596" y="-2.51"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="23.768799" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.10902" y="-2.51"> (</t年代pan> <tspan style="font-size: 12.50px; " x="39.272518" y="-2.51"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="49.024857" y="-2.51"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="60.365078" y="-2.51"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="67.416771" y="-2.51"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,306.39,-232.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 8</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,317.07,-246.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,322.64,-241.41)"> <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="10.869984" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,338.49,-246.41)"> <tspan style="font-size: 12.50px; " x="13.06" y="7.3200002"> 吗?</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="6.6515961" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-245.19" y="39.720001"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-232.46194" y="39.720001"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,114.42,-289.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,119.3,-286.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,124.86,-281.13)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,141.81,-286.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="23.48" y="-8.3000002"> ? ?</t年代pan> </text> <g> <path d="m 154.35,-283.01 28.15,0" 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,-1,154.35,-294.88)"> <tspan style="font-size: 12.50px; " x="31.42" y="-1.42"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="40.799999" y="-8.75"> ? ?</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="9.7398367" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="21.092562" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="49.049999" y="-17.049999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="58.802341" y="-17.049999"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="70.142563" y="-17.049999"> ? ?</t年代pan> </text> <g> <path d="m 203.4,-283.01 28.15,0" 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,-1,210.46,-294.88)"> <tspan style="font-size: 12.50px; " x="25.059999" y="-8.75"> +</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="7.051692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="37.599998" y="-17.049999"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="47.352341" y="-17.049999"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="58.692562" y="-17.049999"> ? ?</t年代pan> </text> <g> <path d="m 248.06,-283.01 28.15,0" 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,-1,258.65,-294.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="18.76" y="-1.42"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-165.35001" y="29.219999"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-152.62195" y="29.219999"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,114.42,-327.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,119.3,-324.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,124.86,-319.1)"> <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="10.922496" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,141.81,-324.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3000002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="18.7915" y="-8.3000002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="25.830688" y="-8.3000002"> ? ?</t年代pan> </text> <g> <path d="m 154.35,-320.98 19.55,0" 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,-1,159.7,-332.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,163.67,-335.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.1,-324.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="292.76999" y="-188.96001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="296.9335" y="-188.96001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="303.185" y="-188.96001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="309.43649" y="-188.96001"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.6" id="M108" style="vertical-align:-3.13504pt;width:43.912498px;" version="1.1" viewbox="0 0 43.912498 14.6" width="43.912498" 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,-63.56,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-55.21,63.5)"> <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="14.6" id="M109" style="vertical-align:-3.13504pt;width:43.912498px;" version="1.1" viewbox="0 0 43.912498 14.6" width="43.912498" 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,-63.56,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-55.21,63.5)"> <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>是常数。由此可见,<年代pan class="equation" id="EEq11"> <svg height="35.912498" id="M110" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 35.912498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,35.9125)"> <g transform="translate(72,-43.27)"> <text transform="matrix(1,0,0,-1,85.54,56.78)"> <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="2.5" y="1.58"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,94.37,52.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,101.32,55.2)"> <tspan style="font-size: 12.50px; " x="12.24" y="-1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="1.58"> |</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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.219999" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.247887" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,139.97,52.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,144.84,55.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.4,60.2)"> <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="10.931248" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,167.35,55.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="13.84" y="-8.3000002"> ? ?</t年代pan> </text> <g> <path d="m 179.89,58.32 8.85,0" 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,-1,179.89,46.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.87,43.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,189.93,55.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.139999" y="-1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="25.139999" y="1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="27.639999" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,223.9,52.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,230.86,55.2)"> <tspan style="font-size: 12.50px; " x="12.24" y="-1.58"> |</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="1.58"> |</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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.209999" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.237886" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,269.5,52.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,274.37,55.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,279.93,60.2)"> <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="10.931248" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,296.88,55.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3000002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="18.7915" y="-8.3000002"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="25.042999" y="-8.3000002"> ? ?</t年代pan> </text> <g> <path d="m 309.42,58.32 19.56,0" 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,-1,314.77,46.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,318.75,43.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,330.17,55.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="137.7" y="0.69"> (</t年代pan> <tspan style="font-size: 12.50px; " x="141.86349" y="0.69"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="148.11501" y="0.69"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="154.3665" y="0.69"> )</t年代pan> </text> </g> </g> </svg></span>自<年代vg height="14.6" id="M111" style="vertical-align:-3.13504pt;width:94.625px;" version="1.1" viewbox="0 0 94.625 14.6" width="94.625" 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,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.28,63.5)"> <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="22.155315" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="33.495537" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="44.435661" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="47.911495" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.39,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.51,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>,我们可以从(<一个href="#EEq11">23</一个>)获得<年代pan class="equation" id="eq24"> <svg height="44.075001" id="M112" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 44.075001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,44.075)"> <g transform="translate(72,-36.74)"> <text transform="matrix(1,0,0,-1,144.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.67"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="24.5"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="12.26"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="40.509998" y="5"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="11.92" y="12.25"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.0835" y="12.25"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="19.996939" y="12.25"> )</t年代pan> <tspan style="font-size: 12.50px; " x="26.936104" y="12.25"> +</t年代pan> </text> <g> <path d="m 184.39,54.37 8.85,0" 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,-1,184.39,42.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.36,39.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,194.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.67"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="24.5"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.98" y="12.26"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.007887" y="12.26"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,220.83,48.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,225.71,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,231.27,56.25)"> <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="10.931248" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,248.22,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="13.84" y="-8.3100004"> ? ?</t年代pan> </text> <g> <path d="m 260.76,54.37 8.85,0" 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,-1,260.76,42.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,264.73,39.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,270.8,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="197.07001" y="-0.0099999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="201.23351" y="-0.0099999998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="207.485" y="-0.0099999998"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="213.7365" y="-0.0099999998"> )</t年代pan> </text> </g> </g> </svg></span>这部分显示,球的半径<年代vg height="14.6" id="M113" style="vertical-align:-3.13504pt;width:54.325001px;" version="1.1" viewbox="0 0 54.325001 14.6" width="54.325001" 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="8.5645552" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="26.856443" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="30.332277" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.63,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>与中心位于<年代vg height="14.6" id="M114" style="vertical-align:-3.13504pt;width:53.950001px;" version="1.1" viewbox="0 0 53.950001 14.6" width="53.950001" 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> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.56,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.52,63.5)"> <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>是一个吸引子<年代vg height="14.3625" id="M115" style="vertical-align:-3.2316pt;width:21.9125px;" version="1.1" viewbox="0 0 21.9125 14.3625" width="21.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <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,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> 1</t年代pan> </text> </g> </g> </svg>。类似的工作,我们有,当<年代vg height="13.45" id="M116" style="vertical-align:-2.21957pt;width:51.799999px;" version="1.1" viewbox="0 0 51.799999 13.45" width="51.799999" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" 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="35.08342" y="0"> 0</t年代pan> </text> </g> </g> </svg>,球的半径<我>r</gydF4y2Ba我>,位于中心<年代vg height="14.6" id="M117" style="vertical-align:-3.13504pt;width:59.450001px;" version="1.1" viewbox="0 0 59.450001 14.6" width="59.450001" 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> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="19.504681" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="22.980515" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.99,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.12,63.5)"> <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>作为另一个吸引子<年代vg height="14.3625" id="M118" style="vertical-align:-3.2316pt;width:21.9125px;" version="1.1" viewbox="0 0 21.9125 14.3625" width="21.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <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,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> 2</t年代pan> </text> </g> </g> </svg>。选择增益<年代vg height="10.7375" id="M119" 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>以满足不等式<年代vg height="13.425" id="M120" style="vertical-align:-2.29482pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 13.425" width="35.799999" 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="10.239957" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>然后我们有<年代pan class="equation" id="eq25"> <svg height="38.575001" id="M121" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,64.66,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="11.61" y="-14.58"> ? ?</t年代pan> </text> <g> <path d="m 75.24,56.57 8.85,0" 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,-1,75.24,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,79.21,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,88.06,53.45)"> <tspan style="font-size: 12.50px; " x="16.440001" y="7.3299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="29.299999" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="43.57" y="-7.25"> ? ?</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> </text> <g> <path d="m 130.59,56.57 8.85,0" 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,-1,130.59,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,134.56,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,143.41,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="13.84" y="-8.3000002"> ? ?</t年代pan> </text> <g> <path d="m 155.95,56.57 8.85,0" 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,-1,155.95,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,159.93,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,169.47,53.45)"> <tspan style="font-size: 12.50px; " x="43.419998" y="7.3299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="52.799999" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="63.599998" y="-7.25"> ? ?</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="18.279387" y="0"> ,</t年代pan> </text> <g> <path d="m 232.03,56.57 8.85,0" 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,-1,232.03,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,236.01,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,244.86,53.45)"> <tspan style="font-size: 12.50px; " x="16.440001" y="7.3299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="29.290001" 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="11.327718" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="42.52" y="-7.25"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="51.084557" y="-7.25"> ? ?</t年代pan> </text> <g> <path d="m 287.38,56.57 15.35,0" 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,-1,290.63,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,294.61,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,306.7,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="13.84" y="-8.3000002"> ? ?</t年代pan> </text> <g> <path d="m 319.24,56.57 8.85,0" 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,-1,319.24,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,323.21,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,332.76,53.45)"> <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="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="135.11" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="139.2735" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="145.52499" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="151.7765" y="0"> )</t年代pan> </text> </g> </g> </svg></span>它遵循从上面的两个两个流动的不平等<年代vg height="14.3625" id="M122" style="vertical-align:-3.2316pt;width:21.9125px;" version="1.1" viewbox="0 0 21.9125 14.3625" width="21.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <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,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.3625" id="M123" style="vertical-align:-3.2316pt;width:21.9125px;" version="1.1" viewbox="0 0 21.9125 14.3625" width="21.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <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,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> 2</t年代pan> </text> </g> </g> </svg>不相交,摄动系统的行为<一个href="#EEq9">15</一个>)将定性类似于标称系统的行为。因此,摄动系统收敛于原点名义系统的以同样的方式和条件<年代vg height="13.45" id="M124" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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="7.3267579" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.490257" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.403696" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M125" style="vertical-align:-2.21957pt;width:24.6px;" version="1.1" viewbox="0 0 24.6 13.45" width="24.6" 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,-65.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="0.78768897" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.9511881" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.8646269" y="0"> )</t年代pan> </text> </g> </g> </svg>可以保证在有限时间内收敛到零。我们完成引理的证明。</年代pan></p> <p><span class="statement" id="thm1"><span class="statement-title">定理3。</年代pan><i>考虑系统(<一个href="#EEq1">1</一个>)和滑动变量(<一个href="#EEq2">2</一个>)和控制输入(<一个href="#EEq4">4</一个>)。让<年代vg height="14.8375" id="M126" style="vertical-align:-3.13504pt;width:80.199997px;" version="1.1" viewbox="0 0 80.199997 14.8375" width="80.199997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8375)"> <g transform="translate(72,-60.13)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <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"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.91,60.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.04,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="16.266403" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="24.605904" y="0"> 吗?</t年代pan> </text> </g> </g> </svg>。如果这些矩阵的元素<年代vg height="14.6" id="M127" style="vertical-align:-3.13504pt;width:16.637501px;" version="1.1" viewbox="0 0 16.637501 14.6" width="16.637501" 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,-63.61,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.6" id="M128" style="vertical-align:-3.13504pt;width:16.637501px;" version="1.1" viewbox="0 0 16.637501 14.6" width="16.637501" 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,-63.61,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.6875" id="M129" style="vertical-align:-0.0pt;width:12.2875px;" version="1.1" viewbox="0 0 12.2875 10.6875" width="12.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <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> </g> </g> </svg>满足下列条件:</我><年代pan class="equation" id="EEq12"> <svg height="37.625" id="M130" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.625)"> <g transform="translate(72,-41.9)"> <text transform="matrix(1,0,0,-1,112.36,50.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,116.33,47.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,127.4,50.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.25"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,144.86,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.25" y="9.21"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.1259999" y="9.21"> ? ?</t年代pan> </text> <g> <path d="m 140.64,53.83 11.57,0" 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,-1,143.3,41.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="10.1" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="35.23103" y="-8.7600002"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,185.32,47.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.01,50.71)"> <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="18.279387" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="33.458027" y="0"> f</t年代pan> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="43.485435" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="51.799931" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="59.164196" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="71.204582" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="77.456085" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="82.657333" y="0"> …</t年代pan> <tspan style="font-size: 12.50px; " x="97.248337" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="102.46208" 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="275.85999" y="-3.1199999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="280.0235" y="-3.1199999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="286.27499" y="-3.1199999"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="292.52649" y="-3.1199999"> )</t年代pan> </text> </g> </g> </svg></span><i>那么一个可以显示系统状态渐近方法为零。</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>我们第一次表达系统(<一个href="#EEq7">7</一个>)为一组二阶系统的形式<年代pan class="equation" id="EEq13"> <svg height="46.1875" id="M131" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 46.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,46.1875)"> <g transform="translate(72,-35.05)"> <text transform="matrix(1,0,0,-1,90.74,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-5.6138468" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,90.62,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,95.92,61.14)"> <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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="15.016103" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="26.356323" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,126.26,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,140.08,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-6.2139912" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="1.36" y="-0.0099999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="5.523499" y="-0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.4369383" y="-0.0099999998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="16.376102" y="-0.0099999998"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.716324" y="-0.0099999998"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,171.78,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,179.37,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="7.5900002" y="-0.0099999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.753499" y="-0.0099999998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.666938" y="-0.0099999998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="23.293768" y="-0.0099999998"> =</t年代pan> <tspan style="font-size: 12.50px; " x="35.334156" y="-0.0099999998"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="43.898712" y="-0.0099999998"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,230.05,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,235.36,61.13)"> <tspan style="font-size: 12.50px; " x="27.09" y="2.51"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.939999" y="0"> ? ?</t年代pan> <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"> g</t年代pan> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,273.8,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,279.11,61.14)"> <tspan style="font-size: 12.50px; " x="12.24" y="2.52"> 吗?</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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="20.870001" y="0.0099999998"> +</t年代pan> <tspan style="font-size: 12.50px; " x="32.19772" y="0.0099999998"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,318.26,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,323.56,61.14)"> <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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-69.080002" y="22.290001"> f</t年代pan> <tspan style="font-size: 12.50px; " x="-65.316597" y="22.290001"> o</t年代pan> <tspan style="font-size: 12.50px; " x="-59.065098" y="22.290001"> r</t年代pan> <tspan style="font-size: 12.50px; " x="-50.738098" y="22.290001"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="-43.373833" y="22.290001"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-31.345945" y="22.290001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-25.094446" y="22.290001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-19.880695" y="22.290001"> …</t年代pan> <tspan style="font-size: 12.50px; " x="-5.2896938" y="22.290001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-0.088445999" y="22.290001"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="8.7886839" y="22.290001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="144.31" y="10.74"> (</t年代pan> <tspan style="font-size: 12.50px; " x="148.4735" y="10.74"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="154.72501" y="10.74"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="160.9765" y="10.74"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.7125" id="M132" style="vertical-align:-3.2316pt;width:61.575001px;" version="1.1" viewbox="0 0 61.575001 14.7125" width="61.575001" 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="2.5006001" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.29,63.5)"> <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="8.0769377" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="18.204369" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.244757" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M133" style="vertical-align:-1.76814pt;width:74.537498px;" version="1.1" viewbox="0 0 74.537498 12.8875" width="74.537498" 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,-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="7.3517642" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" 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="45.435902" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="50.649654" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>在哪里<年代vg height="14.8375" id="M134" style="vertical-align:-3.13504pt;width:107.4px;" version="1.1" viewbox="0 0 107.4 14.8375" width="107.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8375)"> <g transform="translate(72,-60.13)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <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"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.91,60.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.04,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="6.5390692" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="16.266403" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="24.605904" y="0"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="34.620808" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="46.648693" y="0"> 0</t年代pan> </text> </g> </g> </svg>是一个已知的常数。应用引理的结果<一个href="#lem2">2</一个>到(<一个href="#EEq13">27</一个>),如果参数<年代vg height="14.5875" id="M135" style="vertical-align:-3.2316pt;width:14.5875px;" version="1.1" viewbox="0 0 14.5875 14.5875" width="14.5875" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.5875" id="M136" style="vertical-align:-3.2316pt;width:14.5875px;" version="1.1" viewbox="0 0 14.5875 14.5875" width="14.5875" 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,-67.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 2</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.5875" id="M137" style="vertical-align:-3.2316pt;width:12.625px;" version="1.1" viewbox="0 0 12.625 14.5875" width="12.625" 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,-65.17,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>可以满足<年代pan class="equation" id="eq28"> <svg height="37.625" id="M138" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.625)"> <g transform="translate(72,-41.9)"> <text transform="matrix(1,0,0,-1,112.36,50.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,116.33,47.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,127.4,50.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.25"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,144.86,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.25" y="9.21"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.1259999" y="9.21"> ? ?</t年代pan> </text> <g> <path d="m 140.64,53.83 11.57,0" 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,-1,143.3,41.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="10.1" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="35.23103" y="-8.7600002"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,185.32,47.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.01,50.71)"> <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="18.279387" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="33.458027" y="0"> f</t年代pan> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="43.485435" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="51.799931" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="59.164196" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="71.204582" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="77.456085" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="82.657333" y="0"> …</t年代pan> <tspan style="font-size: 12.50px; " x="97.248337" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="102.46208" 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="275.85999" y="-3.1199999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="280.0235" y="-3.1199999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="286.27499" y="-3.1199999"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="292.52649" y="-3.1199999"> )</t年代pan> </text> </g> </g> </svg></span>然后<年代vg height="14.7125" id="M139" style="vertical-align:-3.2316pt;width:26.325001px;" version="1.1" viewbox="0 0 26.325001 14.7125" width="26.325001" 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,-66.45,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.23,63.5)"> <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="8.0769377" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.7125" id="M140" style="vertical-align:-3.2316pt;width:26.325001px;" version="1.1" viewbox="0 0 26.325001 14.7125" width="26.325001" 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,-66.32,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="-5.6263499" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.45,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.23,63.5)"> <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="8.0769377" y="0"> )</t年代pan> </text> </g> </g> </svg>根据引理在有限时间渐近收敛于零<一个href="#lem2">2</一个>。当条件<年代vg height="13.6375" id="M141" style="vertical-align:-2.21957pt;width:48.712502px;" version="1.1" viewbox="0 0 48.712502 13.6375" width="48.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <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="4.863667" y="0"> (</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="12.940605" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="20.567434" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.607822" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>保证,它遵循从等效控制的概念<一个href="#B1">1</一个>,<gydF4y2Ba一个href="#B2">2</一个>]在滑模系统动力学<年代pan class="equation" id="eq29"> <svg height="19.924999" id="M142" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.925)"> <g transform="translate(72,-56.06)"> <text transform="matrix(1,0,0,-1,133.71,60.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="30.209999" y="2.6500001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-6.1300001" y="0.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.4595611" y="0.13"> (</t年代pan> <tspan style="font-size: 12.50px; " x="6.6230602" y="0.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.536499" y="0.13"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.163328" y="0.13"> =</t年代pan> <tspan style="font-size: 12.50px; " x="36.060001" y="0.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="47.862831" y="0.13"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="59.203053" y="0.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="67.542557" y="0.13"> (</t年代pan> <tspan style="font-size: 12.50px; " x="71.706055" y="0.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="81.433388" y="0.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="89.772888" y="0.13"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.66,66.03)"> <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,-1,238.52,60.68)"> <tspan style="font-size: 12.50px; " x="18.76" y="2.52"> 吗?</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="9.727334" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="26.690001" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="35.27956" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="39.443062" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="43.356499" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="49.595497" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="229.35001" y="-0.23"> (</t年代pan> <tspan style="font-size: 12.50px; " x="233.5135" y="-0.23"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="239.765" y="-0.23"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="246.01649" y="-0.23"> )</t年代pan> </text> </g> </g> </svg></span>因为矩阵的非零特征值<年代vg height="16.987499" id="M143" style="vertical-align:-2.21957pt;width:109.5125px;" version="1.1" viewbox="0 0 109.5125 16.987499" width="109.5125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.9875)"> <g transform="translate(72,-58.41)"> <text transform="matrix(1,0,0,-1,-71.95,60.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="31.482553" 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="45.373386" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="53.712887" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.07,66.03)"> <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,-3.2,60.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>放置在左中场平面,我们可以得出结论:系统的状态渐近方法为零,最后完成定理的证明。</年代pan></p> <h4 id="numerical-example">4所示。数值例子</gydF4y2Bah4> <p>为了演示了该方法的有效性,我们考虑一个不稳定的批量反应堆的匹配干扰引入系统及其状态空间形式给出的<年代pan class="equation" id="eq30"> <svg height="261.39999" id="M144" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 261.39999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,261.4)"> <g transform="translate(72,137.12)"> <text transform="matrix(1,0,0,-1,81.04,18.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"></tspan> <tspan style="font-size: 12.50px; " x="32.990002" y="-37.939999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.990002" y="-26.15"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.990002" y="-14.36"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.990002" y="-2.5699999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.990002" y="9.2200003"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.990002" y="21.01"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.990002" y="32.810001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="32.990002" y="44.529999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="-37.939999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="-26.15"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="-14.36"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="-2.5699999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="9.2200003"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="21.01"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="32.799999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="215.84" y="44.529999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="33.689999" y="109.13"> +</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="71.050003"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="82.839996"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="94.629997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="106.42"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="118.21"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="130"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="141.8"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="45.029999" y="153.53"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="71.050003"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="82.839996"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="94.629997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="106.42"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="118.21"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="130"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="141.8"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="121.46" y="153.53"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="129.17" y="95.43"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="129.17" y="106.69"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="129.17" y="117.95"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="129.17" y="129.14"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="170.2" y="95.43"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="170.2" y="106.69"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="170.2" y="117.95"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="170.2" y="129.14"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="212.31" y="127.8"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="-6.1199999" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="2.457058" y="0.14"> (</t年代pan> <tspan style="font-size: 12.50px; " x="6.6205568" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="10.533996" y="0.14"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.173328" y="0.14"> =</t年代pan> <tspan style="font-size: 12.50px; " x="49.150002" y="-35.5"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="55.401501" y="-35.5"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="58.527248" y="-35.5"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="64.778748" y="-35.5"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="87.53421" y="-35.5"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="96.098763" y="-35.5"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="102.35027" y="-35.5"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="105.47601" y="-35.5"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="111.72752" y="-35.5"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="117.97901" y="-35.5"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="124.23051" y="-35.5"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="140.74698" y="-35.5"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="146.99847" y="-35.5"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="150.12422" y="-35.5"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="156.37573" y="-35.5"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="162.62723" y="-35.5"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="179.1312" y="-35.5"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="187.69574" y="-35.5"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="193.94725" y="-35.5"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="197.073" y="-35.5"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="203.32449" y="-35.5"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="209.57599" y="-35.5"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="38.619999" y="-10.49"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="47.184555" y="-10.49"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="53.436054" y="-10.49"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="56.561806" y="-10.49"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="62.813305" y="-10.49"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="69.064804" y="-10.49"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="75.316307" y="-10.49"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="93.783234" y="-10.49"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="102.34779" y="-10.49"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="108.59929" y="-10.49"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="111.72504" y="-10.49"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="117.97654" y="-10.49"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="151.68463" y="-10.49"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="183.41724" y="-10.49"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="189.66875" y="-10.49"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="192.79449" y="-10.49"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="199.04599" y="-10.49"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="205.2975" y="-10.49"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="46.029999" y="14.52"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="52.281502" y="14.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="55.407249" y="14.52"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="61.658749" y="14.52"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="67.910248" y="14.52"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="94.941734" y="14.52"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="101.19324" y="14.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="104.31898" y="14.52"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="110.57049" y="14.52"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="116.82198" y="14.52"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="136.4642" y="14.52"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="145.02875" y="14.52"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="151.28026" y="14.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="154.40601" y="14.52"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="160.6575" y="14.52"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="166.909" y="14.52"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="183.42546" y="14.52"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="189.67697" y="14.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="192.80272" y="14.52"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="199.05421" y="14.52"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="205.30571" y="14.52"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="46.029999" y="39.52"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="52.281502" y="39.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="55.407249" y="39.52"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="61.658749" y="39.52"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="67.910248" y="39.52"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="94.941734" y="39.52"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="101.19324" y="39.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="104.31898" y="39.52"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="110.57049" y="39.52"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="116.82198" y="39.52"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="140.74022" y="39.52"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="146.99173" y="39.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="150.11748" y="39.52"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="156.36897" y="39.52"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="162.62047" y="39.52"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="179.13693" y="39.52"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="187.70149" y="39.52"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="193.95299" y="39.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="197.07875" y="39.52"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="203.33025" y="39.52"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="209.58174" y="39.52"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="223.55" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="232.12706" y="0.14"> (</t年代pan> <tspan style="font-size: 12.50px; " x="236.29056" y="0.14"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="240.20399" y="0.14"> )</t年代pan> <tspan style="font-size: 12.50px; " x="61.599998" y="73.5"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="99.984207" y="73.5"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="50.66" y="98.5"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="56.911499" y="98.5"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="60.037251" y="98.5"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="66.28875" y="98.5"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="72.540253" y="98.5"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="99.984337" y="98.5"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="50.66" y="123.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="56.911499" y="123.51"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="60.037251" y="123.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="66.28875" y="123.51"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="72.540253" y="123.51"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="84.755684" y="123.51"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="93.320236" y="123.51"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="99.571739" y="123.51"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="102.69749" y="123.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="108.94898" y="123.51"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="115.20049" y="123.51"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="50.66" y="148.50999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="56.911499" y="148.50999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="60.037251" y="148.50999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="66.28875" y="148.50999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="72.540253" y="148.50999"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="99.984337" y="148.50999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="134.8" y="109.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="143.82716" y="109.13"> (</t年代pan> <tspan style="font-size: 12.50px; " x="147.99066" y="109.13"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="151.9041" y="109.13"> )</t年代pan> <tspan style="font-size: 12.50px; " x="158.84326" y="109.13"> +</t年代pan> <tspan style="font-size: 12.50px; " x="175.82001" y="97.879997"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="182.0715" y="97.879997"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="185.19725" y="97.879997"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="193.52425" y="97.879997"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="198.38791" y="97.879997"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="201.86375" y="97.879997"> n</t年代pan> <tspan style="font-size: 12.50px; " x="216.46001" y="97.870003"> (</t年代pan> <tspan style="font-size: 12.50px; " x="220.6235" y="97.870003"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="226.875" y="97.870003"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="230.00075" y="97.870003"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="236.25224" y="97.870003"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="240.1657" y="97.870003"> )</t年代pan> <tspan style="font-size: 12.50px; " x="178.97" y="122.88"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="187.297" y="122.88"> c</t年代pan> <tspan style="font-size: 12.50px; " x="192.84833" y="122.88"> o</t年代pan> <tspan style="font-size: 12.50px; " x="199.09982" y="122.88"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="220.87" y="115.63"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="228.45932" y="115.63"> ? ?</t年代pan> </text> <g> <path d="m 301.91,-100.81 11.52,0" 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,-1,304.54,-112.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.08" y="-3.8299999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="20.83" y="-36.200001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="20.83" y="-24.940001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="20.83" y="-13.68"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="20.83" y="-2.49"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="26.459999" y="-36.200001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="26.459999" y="-24.940001"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="26.459999" y="-13.68"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="26.459999" y="-2.49"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="34.169998" y="-22.5"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="163.33" y="-77"> (</t年代pan> <tspan style="font-size: 12.50px; " x="167.4935" y="-77"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="173.745" y="-77"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="179.99651" y="-77"> )</t年代pan> </text> </g> </g> </svg></span>滑动变量选择<年代pan class="equation" id="eq31"> <svg height="62.637501" id="M145" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 62.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,62.6375)"> <g transform="translate(72,-21.89)"> <text transform="matrix(1,0,0,-1,86.08,43.82)"> <tspan style="font-size: 12.50px; " x="34.700001" y="-13.08"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="34.700001" y="-2.23"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="34.700001" y="8.6099997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="34.700001" y="19.4"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="212.92999" y="-13.08"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="212.92999" y="-2.23"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="212.92999" y="8.6099997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="212.92999" y="19.4"> 吗?</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="6.9391651" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="15.016103" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="22.655436" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="40.330002" y="-10.63"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="48.894554" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="55.146053" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="58.271805" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="64.523308" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="70.774803" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="77.026306" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="89.254242" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="95.505737" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="98.631493" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="104.88299" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="111.13449" y="-10.63"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="117.38599" y="-10.63"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="147.95583" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="178.53816" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="184.78966" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="187.91541" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="194.16692" y="-10.63"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="200.41841" y="-10.63"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="206.66991" y="-10.63"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="40.330002" y="14.38"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="48.894554" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="55.146053" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="58.271805" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="64.523308" y="14.38"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="70.774803" y="14.38"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="77.026306" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="89.254242" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="95.505737" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="98.631493" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="104.88299" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="111.13449" y="14.38"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="117.38599" y="14.38"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="129.61392" y="14.38"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="138.17848" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="144.42998" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="147.55573" y="14.38"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="153.80722" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="160.05873" y="14.38"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="166.31023" y="14.38"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="178.53816" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="184.78966" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="187.91541" y="14.38"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="194.16692" y="14.38"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="200.41841" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="206.66991" y="14.38"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="220.64" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="229.21706" y="7.1054274e-015"> (</t年代pan> <tspan style="font-size: 12.50px; " x="233.38055" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="237.29399" y="7.1054274e-015"> )</t年代pan> <tspan style="font-size: 12.50px; " x="243.53299" y="7.1054274e-015"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="381.79001" y="7.1054274e-015"> (</t年代pan> <tspan style="font-size: 12.50px; " x="385.95349" y="7.1054274e-015"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="392.20499" y="7.1054274e-015"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="398.45651" y="7.1054274e-015"> )</t年代pan> </text> </g> </g> </svg></span>的非零特征值系统在滑模分配<年代vg height="13.575" id="M146" style="vertical-align:-2.26974pt;width:58.674999px;" version="1.1" viewbox="0 0 58.674999 13.575" width="58.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="14.565995" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="20.817495" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="26.018744" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="34.583298" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="40.834797" y="0"> }</t年代pan> </text> </g> </g> </svg>。我们设计的传统滑模控制器和边界层控制器,分别<年代pan class="equation" id="eq32"> <svg height="190.03751" id="M147" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 190.03751" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,190.0375)"> <g transform="translate(72,80.03)"> <text transform="matrix(1,0,0,-1,74.91,43.82)"> <tspan style="font-size: 12.50px; " x="51.610001" y="-13.08"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="-2.23"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="8.6099997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="19.4"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="-13.08"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="-2.23"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="8.6099997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="19.4"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="67.370003"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="78.209999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="89.059998"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="99.849998"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="67.370003"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="78.209999"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="89.059998"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="99.849998"> 吗?</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="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="17.104103" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.743437" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="40.259659" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="57.23" y="-10.63"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="65.794556" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.046059" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.171806" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="81.423302" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="87.674805" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="93.926308" y="-10.63"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="106.15424" y="-10.63"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="114.7188" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="120.97029" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="124.09605" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="130.34755" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="136.59904" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="142.85054" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="157.04144" y="-10.63"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="165.606" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="171.8575" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="174.98326" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="181.23476" y="-10.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="199.71419" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="205.96568" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="209.09143" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="215.34294" y="-10.63"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="221.59444" y="-10.63"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="227.84593" y="-10.63"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="57.23" y="14.38"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="65.794556" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.046059" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.171806" y="14.38"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="81.423302" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="87.674805" y="14.38"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="93.926308" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="106.15424" y="14.38"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="114.7188" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="120.97029" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="124.09605" y="14.38"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="130.34755" y="14.38"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="136.59904" y="14.38"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="142.85054" y="14.38"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="155.07848" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="161.32997" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="164.45573" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="170.70723" y="14.38"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="176.95872" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="183.21024" y="14.38"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="195.43816" y="14.38"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="204.00272" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="210.25421" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="213.37997" y="14.38"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="219.63147" y="14.38"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="225.88297" y="14.38"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="232.13446" y="14.38"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="246.10001" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="254.67706" y="7.1054274e-015"> (</t年代pan> <tspan style="font-size: 12.50px; " x="258.84055" y="7.1054274e-015"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="262.754" y="7.1054274e-015"> )</t年代pan> <tspan style="font-size: 12.50px; " x="40.259998" y="39.599998"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="51.60022" y="39.599998"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="59.93972" y="39.599998"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="64.803391" y="39.599998"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="68.279221" y="39.599998"> g</t年代pan> <tspan style="font-size: 12.50px; " x="74.530724" y="39.599998"> n</t年代pan> <tspan style="font-size: 12.50px; " x="87.033722" y="39.599998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="91.19722" y="39.599998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="98.136391" y="39.599998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="102.29989" y="39.599998"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="106.21333" y="39.599998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="110.37682" y="39.599998"> )</t年代pan> <tspan style="font-size: 12.50px; " x="116.62833" y="39.599998"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-0" y="80.449997"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="80.449997"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="80.449997"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="80.449997"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.743437" y="80.449997"> =</t年代pan> <tspan style="font-size: 12.50px; " x="40.259659" y="80.449997"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="57.23" y="69.82"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="65.794556" y="69.82"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.046059" y="69.82"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.171806" y="69.82"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="81.423302" y="69.82"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="87.674805" y="69.82"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="93.926308" y="69.82"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="106.15424" y="69.82"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="114.7188" y="69.82"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="120.97029" y="69.82"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="124.09605" y="69.82"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="130.34755" y="69.82"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="136.59904" y="69.82"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="142.85054" y="69.82"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="157.04144" y="69.82"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="165.606" y="69.82"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="171.8575" y="69.82"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="174.98326" y="69.82"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="181.23476" y="69.82"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="199.71419" y="69.82"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="205.96568" y="69.82"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="209.09143" y="69.82"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="215.34294" y="69.82"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="221.59444" y="69.82"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="227.84593" y="69.82"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="57.23" y="94.830002"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="65.794556" y="94.830002"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.046059" y="94.830002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.171806" y="94.830002"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="81.423302" y="94.830002"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="87.674805" y="94.830002"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="93.926308" y="94.830002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="106.15424" y="94.830002"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="114.7188" y="94.830002"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="120.97029" y="94.830002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="124.09605" y="94.830002"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="130.34755" y="94.830002"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="136.59904" y="94.830002"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="142.85054" y="94.830002"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="155.07848" y="94.830002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="161.32997" y="94.830002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="164.45573" y="94.830002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="170.70723" y="94.830002"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="176.95872" y="94.830002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="183.21024" y="94.830002"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="195.43816" y="94.830002"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="204.00272" y="94.830002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="210.25421" y="94.830002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="213.37997" y="94.830002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="219.63147" y="94.830002"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="225.88297" y="94.830002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="232.13446" y="94.830002"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="246.10001" y="80.449997"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="254.67706" y="80.449997"> (</t年代pan> <tspan style="font-size: 12.50px; " x="258.84055" y="80.449997"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="262.754" y="80.449997"> )</t年代pan> <tspan style="font-size: 12.50px; " x="40.259998" y="120.05"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="51.60022" y="120.05"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="59.93972" y="120.05"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="64.803391" y="120.05"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="70.354721" y="120.05"> t</t年代pan> <tspan style="font-size: 12.50px; " x="80.832237" y="120.05"> (</t年代pan> <tspan style="font-size: 12.50px; " x="84.995735" y="120.05"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="91.934898" y="120.05"> (</t年代pan> <tspan style="font-size: 12.50px; " x="96.098396" y="120.05"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="100.01183" y="120.05"> )</t年代pan> <tspan style="font-size: 12.50px; " x="106.26334" y="120.05"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="111.47709" y="120.05"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="117.72858" y="120.05"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="120.85434" y="120.05"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="127.10583" y="120.05"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="133.35735" y="120.05"> )</t年代pan> <tspan style="font-size: 12.50px; " x="139.59633" y="120.05"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="392.95999" y="50.959999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="397.1235" y="50.959999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="403.375" y="50.959999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="409.6265" y="50.959999"> )</t年代pan> </text> </g> </g> </svg></span>给出了应用该算法的控制输入<年代pan class="equation" id="eq33"> <svg height="112.1125" id="M148" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 112.1125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,112.1125)"> <g transform="translate(72,17.69)"> <text transform="matrix(1,0,0,-1,74.91,43.82)"> <tspan style="font-size: 12.50px; " x="51.610001" y="-13.08"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="-2.23"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="8.6099997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="51.610001" y="19.4"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="-13.08"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="-2.23"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="8.6099997"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="238.39" y="19.4"> 吗?</t年代pan> <tspan style="font-size: 12.50px; " x="105.75" y="57.540001"> 吗?</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="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="17.104103" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.743437" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="40.259659" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="57.23" y="-10.63"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="65.794556" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.046059" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.171806" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="81.423302" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="87.674805" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="93.926308" y="-10.63"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="106.15424" y="-10.63"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="114.7188" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="120.97029" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="124.09605" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="130.34755" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="136.59904" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="142.85054" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="157.04144" y="-10.63"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="165.606" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="171.8575" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="174.98326" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="181.23476" y="-10.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="199.71419" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="205.96568" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="209.09143" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="215.34294" y="-10.63"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="221.59444" y="-10.63"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="227.84593" y="-10.63"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="57.23" y="14.38"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="65.794556" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.046059" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.171806" y="14.38"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="81.423302" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="87.674805" y="14.38"> 3</t年代pan> <tspan 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style="font-size: 12.50px; " x="11.102664" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="17.5042" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="23.755699" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="30.407295" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="39.584499" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="50.937222" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,259.65,8.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 8.75px; " x="-1.26" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,265.35,-6.02)"> <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"> g</t年代pan> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="27.094002" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="31.2575" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="38.196667" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="48.7617" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="52.925198" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="59.176701" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="65.828293" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="72.229828" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="202.52" y="-30.049999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="206.6835" y="-30.049999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="212.935" y="-30.049999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="219.18649" y="-30.049999"> )</t年代pan> </text> </g> </g> </svg></span>三种情况下同时模拟初始条件<年代vg height="16.5" id="M149" style="vertical-align:-2.21957pt;width:135.675px;" version="1.1" viewbox="0 0 135.675 16.5" width="135.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5)"> <g transform="translate(72,-58.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ? ?</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="24.293329" 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="40.497215" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="52.725151" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="67.728752" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="79.081474" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="91.30941" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="97.560905" y="0"> ]</t年代pan> </text> <text transform="matrix(1,0,0,-1,29.78,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ? ?</t年代pan> </text> </g> </g> </svg>仿真是在一个固定的步长为1毫秒。时间响应系统状态的三个案例数据所示<一个href="//www.newsama.com/journals/jcse/2012/564906/fig2/" target="_blank">2</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jcse/2012/564906/fig4/" target="_blank">4</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jcse/2012/564906/fig6/" target="_blank">6</一个>,分别。从这些数据可以看到,该方法获得零稳态误差。数据<一个href="//www.newsama.com/journals/jcse/2012/564906/fig3/" target="_blank">3</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jcse/2012/564906/fig5/" target="_blank">5</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jcse/2012/564906/fig7/" target="_blank">7</一个>分别显示了控制输入的三种情况。说明,我们的控制力不表现出任何抖振效应。滑动的反应变量应用该方法在图<一个href="//www.newsama.com/journals/jcse/2012/564906/fig8/" target="_blank">8</一个>。很明显的图,我们的控制律可以保证滑模的有限时间收敛。结果,仿真结果验证了该战略的良好的性能。</gydF4y2Bap> <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="564906.fig.002" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.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/2012/564906/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 与应用系统状态信号的功能。</t一个ble> </div> </div> </div> <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="564906.fig.003" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.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/2012/564906/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 控制输入应用符号函数。</t一个ble> </div> </div> </div> <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="" name="564906.fig.004" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.fig.004.jpg"> <br> <strong></strong> </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/2012/564906/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 系统状态应用饱和函数。</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="" name="564906.fig.005" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.fig.005.jpg"> <br> <strong></strong> </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/2012/564906/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 控制输入饱和函数中的应用。</t一个ble> </div> </div> </div> <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="" name="564906.fig.006" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.fig.006.jpg"> <br> <strong></strong> </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/2012/564906/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 该方法与应用系统状态。</t一个ble> </div> </div> </div> <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="" name="564906.fig.007" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.fig.007.jpg"> <br> <strong></strong> </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/2012/564906/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 应用该方法控制输入。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig8"> <div class="floats-partial-content fig-content-fig8"> <div class="partial-carousel--single-image"> <img alt="" name="564906.fig.008" src="https://static-01.hindawi.com/articles/jcse/volume-2012/564906/figures/564906.fig.008.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2012/564906/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 滑动变量与应用方法。</t一个ble> </div> </div> </div> <h4 id="conclusions">5。结论</gydF4y2Bah4> <p>在本文中,我们提出了修改后的二阶滑模控制算法来避免MIMO不确定系统的抖振问题。发达的方法不需要滑动变量的导数,从而消除的要求设计一个微分器。根据该动态滑模控制器,我们表明,有限时间收敛滑模保证和系统状态可以渐近方法为零。仿真结果表明,该控制方案展览相当良好的系统性能。</gydF4y2Bap> </div> <div class="xml-content"> <h4 class="references" id="references">引用</gydF4y2Bah4> <ol> <li id="B1">c·爱德华兹和s . k . 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Pydynowski”改进,喋喋不休免费,V.S.C.方案不确定的动力系统,”<我>IEEE自动控制</我>第41卷。。8,1220 - 1226年,1996页。<年代pan class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=An%20improved,%20chattering%20free,%20V.S.C.%20scheme%20for%20uncertain%20dynamical%20systems&author=G. Bartolini &author=P. Pydynowski&publication_year=1996" target="_blank">谷歌学术搜索</一个></年代pan></li> <li id="B12">a·g·Bartolini费拉拉,大肠Usai“由二阶滑模控制,避免喋喋不休”<我>IEEE自动控制</我>,43卷,不。2、241 - 246年,1998页。<年代pan class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Chattering%20avoidance%20by%20second-order%20sliding%20mode%20control&author=G. Bartolini&author=A. Ferrara&author=&author=E. 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Yang&publication_year=2007" target="_blank">谷歌学术搜索</一个></年代pan></li> <li id="B15">a .黎凡特”滑动秩序和滑动在滑模控制精度,”<我>国际期刊的控制</我>58卷,第1263 - 1247页,1993年。<年代pan class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Sliding%20order%20and%20sliding%20accuracy%20in%20the%20sliding%20mode%20control&author=A. Levant&publication_year=1993" target="_blank">谷歌学术搜索</一个></年代pan></li> <li id="B16">黎凡特,“高阶滑动模式,差异化和输出反馈控制,”<我>国际期刊的控制</我>,卷76,不。9 - 10,924 - 941年,2003页。<年代pan class="reflinks">视图:<一个href="https://doi.org/10.1080/0020717031000099029">出版商的网站</一个><年代pan class="sep">|</年代pan><a href="https://scholar.google.com/scholar_lookup?title=Higher-order%20sliding%20modes,%20differentiation%20and%20output-feedback%20control&author=A. 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Levant" target="_blank">谷歌学术搜索</一个></年代pan></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</gydF4y2Bah4> <p>版权©2012 Jeang-Lin常。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</gydF4y2Bap> </div> </div> </article> </div> </div> </div> <div class="biblio__StyledBibblio-sc-1nou1lz-0 eSVfHT"> <div id="takeover" class="biblio__TakeoverWrapper-sc-1nou1lz-2 htjhiS"> <div id="bib--hide-takeover-element-mobile"> <div id="bib--takeover-element-mobile"> <h4 class="biblio__H4-sc-1nou1lz-4 lhUKwc">相关文章</gydF4y2Bah4> <div id="bib--rcm-takeover-element-mobile"> 对本文没有相关内容可用。</d我v> </div> </div> </div> </div> <div class="biblio__StyledBibblio-sc-1nou1lz-0 eSVfHT"> <div class="biblio__FooterWrapper-sc-1nou1lz-3 etZutQ mobile-widget" id="related-articles-hidden"> <div id="bib--hide-footer-element-mobile"> <hr class="biblio__HR-sc-1nou1lz-5 bkemVQ"> <h4 class="biblio__H4-sc-1nou1lz-4 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src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOnhsaW5rPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5L3hsaW5rIiB3aWR0aD0iMjAiIGhlaWdodD0iMjIiIHZpZXdCb3g9IjAgMCAyMCAyMiI+PGRlZnM+PGNsaXBQYXRoIGlkPSJhIj48cGF0aCBkPSJNMywyMmEzLDMsMCwwLDEtMy0zVjE2YTEsMSwwLDAsMSwyLDB2M2ExLDEsMCwwLDAsMSwxSDE3YTEsMSwwLDAsMCwxLTFWMTZhMSwxLDAsMSwxLDIsMHYzYTMsMywwLDAsMS0zLDNabTYuMjg4LTYuMy00LTRhMSwxLDAsMCwxLDEuNDE0LTEuNDE0TDksMTIuNTg2VjFhMSwxLDAsMCwxLDIsMFYxMi41ODZsMi4yOTMtMi4yOTNhMSwxLDAsMCwxLDEuNDE0LDEuNDE0bC00LDRhMSwxLDAsMCwxLTEuNDIzLDBaIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSgyIDEpIi8+PC9jbGlwUGF0aD48L2RlZnM+PGcgdHJhbnNmb3JtPSJ0cmFuc2xhdGUoLTIgLTEpIj48cGF0aCBkPSJNMywyMmEzLDMsMCwwLDEtMy0zVjE2YTEsMSwwLDAsMSwyLDB2M2ExLDEsMCwwLDAsMSwxSDE3YTEsMSwwLDAsMCwxLTFWMTZhMSwxLDAsMSwxLDIsMHYzYTMsMywwLDAsMS0zLDNabTYuMjg4LTYuMy00LTRhMSwxLDAsMCwxLDEuNDE0LTEuNDE0TDksMTIuNTg2VjFhMSwxLDAsMCwxLDIsMFYxMi41ODZsMi4yOTMtMi4yOTNhMSwxLDAsMCwxLDEuNDE0LDEuNDE0bC00LDRhMSwxLDAsMCwxLTEuNDIzLDBaIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSgyIDEpIi8+PGcgY2xpcC1wYXRoPSJ1cmwoI2EpIj48cmVjdCB3aWR0aD0iMjQiIGhlaWdodD0iMjQiIGZpbGw9InJnYmEoMCwwLDAsMCkiLz48cmVjdCB3aWR0aD0iMjQiIGhlaWdodD0iMjQiLz48L2c+PC9nPjwvc3ZnPg==" 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/2012/564906.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> ePub</d我v><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>2983年</年代pan> </div> <div> 下载<年代pan>1560年</年代pan> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2012/564906" data-style="small_circle"></span>引用</d我v> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</gydF4y2Bah3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2012/564906&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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