disturbance rejection level. Secondly, non-fragile sliding mode controller is established to make the state of system reach the sliding surface in a finite time. Finally, an example is given to illustrate the effectiveness of the proposed method.">
非脆弱不确定混沌系统的滑模控制</gydF4y2Batitle>
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no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .gtIExW .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .gtIExW ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .gtIExW ol li{margin:10px 0;padding-left:10px;word-break:normal;} .gtIExW ol li a{word-break:break-all;} .gtIExW ol li .reflinks{display:block;} .gtIExW ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .gtIExW ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .gtIExW ol li .reflinks .sep{color:#000000;} .gtIExW .table-wrapper{width:auto;overflow-x:auto;} .gtIExW .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .gtIExW .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 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<p>在这一页上</p><年代p一个nclass="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p一个n><年代pan 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p一个n><年代pan class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#conclusion" aria-label="">结论</一个></年代p一个n><年代pan 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p一个n><年代pan 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p一个n><年代pan 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p一个n></d我v>
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<p class="sc-kZmsYB bkiEfx article_type">研究文章|<gydF4y2Ba!-- -->开放获取</p><d我v class="sc-RcBXQ ztvYg article_citation">
体积<gydF4y2Ba!-- -->
<!-- -->2011年<gydF4y2Ba!-- -->
<span class="sc-fZwumE cUsFHx">|</年代p一个n>文章的ID<gydF4y2Ba!-- -->
<!-- -->859159年<gydF4y2Ba!-- -->
<span class="sc-fZwumE cUsFHx">|</年代p一个n><一个class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2011/859159" aria-label="Doi-link">https://doi.org/10.1155/2011/859159</一个></d我v>
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<p>韩Leipo Liu Zhengzhi Zhumu傅<gydF4y2Ba!-- -->,<gydF4y2Ba!-- -->
<!-- -->”<年代p一个nclass="adjust-article-svg-size">非脆弱不确定混沌系统的滑模控制</年代p一个n>”,<gydF4y2Ba!-- --><i>控制科学与工程》杂志上</我>,<ggydF4y2BaydF4y2Ba!-- -->
<!-- -->卷。<gydF4y2Ba!-- -->2011年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- -->
<!-- -->文章的ID<gydF4y2Ba!-- -->859159年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- -->
<!-- -->6<gydF4y2Ba!-- -->
<!-- -->
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<!-- -->页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- -->
<!-- -->2011年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- -->
<!-- -->https://doi.org/10.1155/2011/859159</p></d我v>
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<h1 class="sc-iRbamj jZOxOO sc-iSDuPN jVSHWt article_title adjust-article-svg-size heading-title">非脆弱不确定混沌系统的滑模控制</gydF4y2Bah1>
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<span class=""><b>Leipo刘</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>,<年代up>1</gydF4y2Ba年代up></年代p一个n><年代pan class="">Zhengzhi汉<gydF4y2Ba!-- -->,<年代up>2</gydF4y2Ba年代up><!-- -->和</年代p一个n><年代p一个nclass="">Zhumu傅<年代up>1</gydF4y2Ba年代up></年代p一个n><d我v class="sc-fHxwqH dMuGGA isHide">
<p><sup>1</年代up><年代p一个n>电气与信息工程学院、河南科技大学、洛阳471003年,中国</年代p一个n></p><p><sup>2</年代up><年代p一个n>电气与信息工程学院,上海交通大学,200240年上海,中国</年代p一个n></p></d我v>
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<b>学术编辑器:</gydF4y2Bab>偏向可能性</d我v>
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<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">05年4月2011年</年代p一个n></d我v>
<div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished">
<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年6月27日</年代p一个n></d我v>
<div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished">
<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年9月15日</年代p一个n></d我v>
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<article class="sc-jtRlXQ gtIExW article_body ">
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<h4 class="header" id="abstract">文摘</gydF4y2Bah4>
<p>本文是关于非脆弱滑模控制与外部扰动的不确定混沌系统。首先,提出了一种新的滑动面,充分条件导出保证滑模动态与广义渐近稳定<年代vg height="14.2375" id="M1" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>干扰抑制水平。其次,建立了非脆弱滑模控制器使系统状态到达滑动面在一个有限的时间。最后,给出了一个例子来说明该方法的有效性。</p><年代p一个nclass="end-abs"></span>
<h4 id="introduction">1。介绍</gydF4y2Bah4>
<p>混乱的行为是一个看似随机现象的确定性系统的特征是对初始条件敏感deaspendence。许多电子、机械和化学系统表现出混沌动力学。因此,混沌是一个非常有趣的非线性现象,混沌系统的控制已经被研究者重视开创性工作以来奥特et al。<一个href="#B1">1</一个>]。混沌控制的主要目的是抑制混沌行为和稳定混沌系统,以及各种有效的技术已经被提出并成功地应用于获得混沌控制自适应控制等(<一个href="#B2">2</一个>),同步控制(<一个href="#B3">3</一个>,模糊控制<一个href="#B4">4</一个>),最优控制(<一个href="#B5">5</一个>),和滑模控制<一个href="#B6">6</一个>- - - - - -<一个href="#B9">9</一个>]。</p><p>gydF4y2Ba在上述方法中,滑模控制是一种非常有效的方法来控制混乱,因为它有吸引力的特性,比如快速响应,良好的瞬态响应,对系统参数变化和外部扰动的不敏感(<一个href="#B6">6</一个>- - - - - -<一个href="#B11">11</一个>]。此外,在一些工程实践,例如,为了避免执行机构饱和,人们经常保证每当外源输入有界的能量,控制输出应该有一个指定的最大峰值。在这种情况下,广义<年代vg height="14.2375" id="M2" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>控制是一个很好的工具(<一个href="#B12">12</一个>,<gydF4y2Ba一个href="#B13">13</一个>]。</p><p>gydF4y2Ba一般来说,准确的控制器需要稳定控制系统,所以所有的控制器系数是准确值在设计所需的控制器。然而,在实践中,不确定性是不避免,这可能是由于很多原因,如有限字长在数字系统中,模拟系统固有的不精确,需要额外的调优参数在最后控制器实现(<一个href="#B14">14</一个>]。不确定性的存在会导致非脆弱控制问题的研究,也就是说,设计一个控制器,控制器是不确定性不敏感。许多关于非脆弱控制问题已报告的结果(<一个href="#B15">15</一个>- - - - - -<一个href="#B17">17</一个>]。然而,到目前为止,非脆弱不确定混沌系统的滑模控制问题已经很少关注。</p><p>gydF4y2Ba本文不确定混沌系统的非脆弱滑模控制问题与外部扰动。首先,提出了一种新的整型滑动面,并达到阶段消除,和该滑动面功能包括一个norm-bounded参数不确定性;添加这一项的设计不仅使滑动面更放松,但也保证滑模动态有更好的鲁棒性能。加法和乘法的不确定性为例,充分条件导出广义使滑模动态稳定<年代vg height="14.2375" id="M3" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的性能。其次,建立了非脆弱滑模控制器使系统状态到达滑动面在一个有限的时间。最后,给出了一个例子来说明该方法的有效性。</p><p><年代p一个nclass="statement" id="head1"><span class="statement-title"><i class="statement-title">符号</我></年代p一个n><br>本文将使用以下符号。<年代vg height="11.2" id="M4" style="vertical-align:-0.0pt;width:17.75px;" version="1.1" viewbox="0 0 17.75 11.2" width="17.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.2)">
<g transform="translate(72,-63.04)">
<text transform="matrix(1,0,0,-1,-71.95,63.09)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.7,68.09)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="12.1625" id="M5" style="vertical-align:-0.0pt;width:32.525002px;" version="1.1" viewbox="0 0 32.525002 12.1625" width="32.525002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.1625)">
<g transform="translate(72,-62.27)">
<text transform="matrix(1,0,0,-1,-71.95,62.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.7,67.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3497438" y="0">
×</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="9.9510241" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>分别表示<年代vg height="7.1374998" id="M6" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1375)">
<g transform="translate(72,-66.29)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>维欧几里得空间的空间<年代vg height="8.7875004" id="M7" style="vertical-align:-0.3135pt;width:35.9375px;" version="1.1" viewbox="0 0 35.9375 8.7875004" width="35.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,8.7875)">
<g transform="translate(72,-64.97)">
<text transform="matrix(1,0,0,-1,-71.95,65.34)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.9896574" y="0">
×</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.767242" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>真正的矩阵。实对称矩阵<年代vg height="10.325" id="M8" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="11.0625" id="M9" style="vertical-align:-0.30096pt;width:43.037498px;" version="1.1" viewbox="0 0 43.037498 11.0625" width="43.037498" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.028847" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.069235" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>意味着<年代vg height="10.325" id="M10" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是正定的。<年代vg height="14.6" id="M11" style="vertical-align:-3.13504pt;width:56.487499px;" version="1.1" viewbox="0 0 56.487499 14.6" width="56.487499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.22,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">
∞</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.194025" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>空间精确性向量函数结束了吗<年代vg height="13.45" id="M12" style="vertical-align:-2.21957pt;width:39.337502px;" version="1.1" viewbox="0 0 39.337502 13.45" width="39.337502" 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">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">
∞</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.194025" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="14.2375" id="M13" style="vertical-align:-3.13504pt;width:21.9375px;" version="1.1" viewbox="0 0 21.9375 14.2375" width="21.9375" 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">
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</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是必不可少的有界函数的空间。<年代vg height="7.4875002" id="M14" style="vertical-align:-0.0pt;width:8.3000002px;" version="1.1" viewbox="0 0 8.3000002 7.4875002" width="8.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.4875)">
<g transform="translate(72,-66.01)">
<text transform="matrix(1,0,0,-1,-71.95,66.06)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∗</gydF4y2Batspan>
</text>
</g>
</g>
</svg>表示矩阵的对称形式。</年代p一个n></p><h4 id="problem-formulation">2。问题公式化</gydF4y2Bah4>
<p>考虑下面的混沌系统:<年代p一个nclass="equation" id="EEq1">
<svg height="41.349998" id="M15" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,41.35)">
<g transform="translate(72,-38.92)">
<text transform="matrix(1,0,0,-1,91.85,63.2)">
<tspan style="font-size: 12.50px; " x="82.129997" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.6640992" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.2755461" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.439045" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.352484" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.991817" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.032206" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.996857" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.649174" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.989395" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.279602" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.4431" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="85.970627" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.134125" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.01078" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="103.94994" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="115.29016" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.31733" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="134.84485" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.00835" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="145.88501" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="152.82417" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="164.16438" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="172.17882" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="176.34232" y="0">
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<tspan style="font-size: 12.50px; " x="180.25575" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="184.41925" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="191.35841" y="0">
+</gydF4y2Batspan>
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<tspan style="font-size: 12.50px; " x="212.576" y="0">
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(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="228.51733" y="0">
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<tspan style="font-size: 12.50px; " x="232.43077" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="238.68227" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.449997" y="20.469999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="94.613503" y="20.469999">
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)</gydF4y2Batspan>
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=</gydF4y2Batspan>
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<tspan style="font-size: 12.50px; " x="126.58367" y="20.469999">
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<tspan style="font-size: 12.50px; " x="135.54832" y="20.469999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.71182" y="20.469999">
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)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="149.87675" y="20.469999">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="382.26999" y="10.86">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="386.4335" y="10.86">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="392.685" y="10.86">
)</gydF4y2Batspan>
</text>
</g>
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</svg></span>在哪里<年代vg height="13.9625" id="M16" style="vertical-align:-2.21957pt;width:61.037498px;" version="1.1" viewbox="0 0 61.037498 13.9625" width="61.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.9625)">
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)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.580418" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.620808" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.07,68.09)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>状态向量,<年代vg height="13.9625" id="M17" style="vertical-align:-2.21957pt;width:62.174999px;" version="1.1" viewbox="0 0 62.174999 13.9625" width="62.174999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.9625)">
<g transform="translate(72,-60.83)">
<text transform="matrix(1,0,0,-1,-71.95,63.09)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.9264221" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.089921" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.00336" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.63019" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.670578" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-29.02,68.09)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是控制输入。<年代vg height="13.9625" id="M18" style="vertical-align:-2.21957pt;width:60.25px;" version="1.1" viewbox="0 0 60.25 13.9625" width="60.25" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.9625)">
<g transform="translate(72,-60.83)">
<text transform="matrix(1,0,0,-1,-71.95,63.09)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.238997" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.942764" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.983154" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.71,68.09)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是系统的输出。<年代vg height="13.6125" id="M19" style="vertical-align:-2.34499pt;width:27.799999px;" version="1.1" viewbox="0 0 27.799999 13.6125" width="27.799999" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.9391651" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.102664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.979315" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个非线性的实值函数。<年代vg height="13" id="M20" style="vertical-align:-1.76814pt;width:97.800003px;" version="1.1" viewbox="0 0 97.800003 13" width="97.800003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13)">
<g transform="translate(72,-61.6)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.9646511" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.165899" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.867987" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.081738" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.471252" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.848499" y="0">
一个</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.399834" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="57.651333" y="0">
d</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="68.06633" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>与兼容矩阵维度和<年代vg height="13.45" id="M21" style="vertical-align:-2.21957pt;width:39.125px;" version="1.1" viewbox="0 0 39.125 13.45" width="39.125" 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">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.12815" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.329397" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.031487" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是完全可控的。<年代vg height="10.325" id="M22" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>满列秩。<年代vg height="13.45" id="M23" style="vertical-align:-2.21957pt;width:27.5375px;" version="1.1" viewbox="0 0 27.5375 13.45" width="27.5375" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6898251" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.853324" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.766764" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个有界扰动。<年代vg height="13.6125" id="M24" style="vertical-align:-2.34499pt;width:39.087502px;" version="1.1" viewbox="0 0 39.087502 13.6125" width="39.087502" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.966331" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.129829" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.006479" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>代表不确定性情况下,令人满意<年代vg height="13.8625" id="M25" style="vertical-align:-2.37006pt;width:82.675003px;" version="1.1" viewbox="0 0 82.675003 13.8625" width="82.675003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.8625)">
<g transform="translate(72,-60.91)">
<text transform="matrix(1,0,0,-1,-71.95,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.566235" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.5054" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.6689" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.545547" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.709049" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.711449" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.751839" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>与一个积极的常数<年代vg height="9.875" id="M26" style="vertical-align:-2.29482pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 9.875" width="7.9749999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba系统的框图(<一个href="#EEq1">1</一个>)在图给出<一个href="//www.newsama.com/journals/jcse/2011/859159/fig1/" target="_blank">1</一个>。</p><d我v 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="859159.fig.001" src="https://static-01.hindawi.com/articles/jcse/volume-2011/859159/figures/859159.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p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/859159/fig1/" title="" target="_blank"></a>
</div>
<div class="floats-partial-caption-text">
<a href="#EEq1">1</一个><table>
系统的框图()gydF4y2Ba。</gydF4y2Batable>
</div>
</div>
</div>
<p>为未来的讨论下面的前题是必要的。</p><p><年代p一个nclass="statement" id="lem1"><span class="statement-title">引理1(见[<一个href="#B8">8</一个>])。</年代p一个n><我>对于一个给定的矩阵<年代vg height="28.9625" id="M27" style="vertical-align:-8.4331pt;width:84.662498px;" version="1.1" viewbox="0 0 84.662498 28.9625" width="84.662498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,28.9625)">
<g transform="translate(72,-48.83)">
<text transform="matrix(1,0,0,-1,-71.95,57.29)">
<tspan style="font-size: 12.50px; " x="23.639999" y="4.9200001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.590281" y="0">
=</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.49,64.77)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.8,62.58)">
<tspan style="font-size: 6.25px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 6.25px; " x="3.1259999" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-24.58,64.77)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-18.89,62.58)">
<tspan style="font-size: 6.25px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 6.25px; " x="3.1259999" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.49,53.25)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.19,56.75)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 6.25px; " x="-0.61000001" y="6.5300002">
1</gydF4y2Batspan>
<tspan style="font-size: 6.25px; " x="2.516" y="6.5300002">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-24.58,53.25)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-18.89,51.06)">
<tspan style="font-size: 6.25px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 6.25px; " x="3.1259999" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-10.06,52.37)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>与<年代vg height="18.7875" id="M28" style="vertical-align:-4.15945pt;width:62.962502px;" version="1.1" viewbox="0 0 62.962502 18.7875" width="62.962502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.7875)">
<g transform="translate(72,-56.97)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,58.04)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.1,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.06,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.88" y="9.2200003">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.4960001" y="9.2200003">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="18.7875" id="M29" style="vertical-align:-4.15945pt;width:62.962502px;" version="1.1" viewbox="0 0 62.962502 18.7875" width="62.962502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.7875)">
<g transform="translate(72,-56.97)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,58.04)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.1,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.06,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.88" y="9.2200003">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.4960001" y="9.2200003">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,然后下列条件是等价的:</我><年代p一个nclass="list"><span class="list-item"><span class="list-label">(1)</年代p一个n><年代p一个nclass="list-content"><i>
<svg height="11.0625" id="M30" style="vertical-align:-0.30096pt;width:37.487499px;" version="1.1" viewbox="0 0 37.487499 11.0625" width="37.487499" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.590281" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.630671" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,</我></年代p一个n></年代pan><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个nclass="list-content"><i>
<svg height="14.6" id="M31" style="vertical-align:-3.13504pt;width:49.049999px;" version="1.1" viewbox="0 0 49.049999 14.6" width="49.049999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.1,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="19.0375" id="M32" style="vertical-align:-4.15945pt;width:134.9875px;" version="1.1" viewbox="0 0 134.9875 19.0375" width="134.9875" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,57.84)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.79,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.327718" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.32,57.84)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-23.07,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-14.07,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.88" y="9.21">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.4960001" y="9.21">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-3.2,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,5.8,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.88" y="9.21">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.4960001" y="9.21">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,17.65,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,</我></年代p一个n></年代pan><span class="list-item"><span class="list-label">(3)</年代p一个n><年代p一个nclass="list-content"><i>
<svg height="14.6" id="M33" style="vertical-align:-3.13504pt;width:49.049999px;" version="1.1" viewbox="0 0 49.049999 14.6" width="49.049999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.1,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="19.0375" id="M34" style="vertical-align:-4.15945pt;width:134.9875px;" version="1.1" viewbox="0 0 134.9875 19.0375" width="134.9875" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,57.84)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.79,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.327718" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-31.45,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.87" y="9.21">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.506" y="9.21">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-23.07,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-14.07,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.88" y="9.21">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.4960001" y="9.21">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-3.2,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,4.92,57.84)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,17.65,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></年代pan></span><i></i></span></p>
<p><span class="statement" id="lem2"><span class="statement-title">引理2(见[<一个href="#B17">17</一个>])。</年代p一个n><我>让<年代vg height="12.8875" id="M35" style="vertical-align:-1.76814pt;width:27.4375px;" version="1.1" viewbox="0 0 27.4375 12.8875" width="27.4375" 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">
Ω</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3022318" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.50348" y="0">
Γ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="10.475" id="M36" style="vertical-align:-0.0pt;width:10.175px;" version="1.1" viewbox="0 0 10.175 10.475" width="10.175" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
Ξ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>适当的矩阵维度,让<年代vg height="10.6875" id="M37" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" 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">
Ω</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是对称的。然后</我><年代p一个nclass="equation" id="eq1">
<svg height="18.424999" id="M38" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.424999" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.425)">
<g transform="translate(72,-57.26)">
<text transform="matrix(1,0,0,-1,128.31,61.06)">
<tspan style="font-size: 12.50px; " x="0" y="0">
Ω</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.077898" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.418119" y="0">
Γ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.75738" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.38517" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.548668" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.462109" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="56.701103" y="0">
Ξ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.528702" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="78.868927" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="83.032425" y="0">
Γ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.371681" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="101.99947" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="106.16297" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="110.07641" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="116.31541" y="0">
Ξ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.35484" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,256.84,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,267.02,61.06)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="207.10001" y="-0.44">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="211.2635" y="-0.44">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="217.515" y="-0.44">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><i>一个不确定的矩阵<年代vg height="13.45" id="M39" style="vertical-align:-2.21957pt;width:25.0875px;" version="1.1" viewbox="0 0 25.0875 13.45" width="25.0875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.7268538" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.890353" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.803792" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>令人满意的<年代vg height="16.2875" id="M40" style="vertical-align:-2.21957pt;width:89px;" version="1.1" viewbox="0 0 89 16.2875" width="89" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2875)">
<g transform="translate(72,-58.97)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.41,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.7,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.240437" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.967291" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.130791" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.04423" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.671059" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.711449" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>当且仅当存在一个标量<年代vg height="11.0625" id="M41" style="vertical-align:-0.30096pt;width:34.887501px;" version="1.1" viewbox="0 0 34.887501 11.0625" width="34.887501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.5147829" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.555172" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样</我><年代p一个nclass="equation" id="eq2">
<svg height="30.862499" id="M42" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.862499" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,30.8625)">
<g transform="translate(72,-47.31)">
<text transform="matrix(1,0,0,-1,140.83,56.25)">
<tspan style="font-size: 12.50px; " x="0" y="0">
Ω</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.077898" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.418119" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.46957" y="0">
Γ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.80883" y="0">
Γ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,184.98,61.25)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,194.47,56.25)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.54" y="-7.25">
1</gydF4y2Batspan>
</text>
<g>
<path d="m 207.01,59.37 6.25,0" 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,-1,207.11,47.49)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.4300003" y="-6.2399998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.28" y="-8.7600002">
Ξ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,230.43,61.25)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,237.14,56.25)">
<tspan style="font-size: 12.50px; " x="0" y="0">
Ξ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.04" y="2.52">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.370001" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.397886" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.66" y="-0.28">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="236.98" y="-0.28">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="241.14349" y="-0.28">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="247.395" y="-0.28">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><i></i></span></p>
<h4 id="main-results">3所示。主要结果</gydF4y2Bah4>
<p>对于系统(<一个href="#EEq1">1</一个>),首先,一个新的滑动面设计,并给出充分条件保证滑模动态与广义渐近稳定<年代vg height="14.2375" id="M43" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>规范约束<年代vg height="9.9375" id="M44" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。其次,设计非脆弱滑模控制器驱动状态在有限时间内到达滑动面。</p><gydF4y2Bah5 id="sec3.1">3.1。滑动面设计</gydF4y2Bah5>
<p>对于系统(<一个href="#EEq1">1</一个>),我们设计以下整型滑动面功能:<年代p一个nclass="equation" id="EEq2">
<svg height="39.174999" id="M45" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.174999" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,39.175)">
<g transform="translate(72,-40.66)">
<text transform="matrix(1,0,0,-1,58.52,52.96)">
<tspan style="font-size: 12.50px; " x="46.849998" y="7.3299999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.19" y="7.6999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.576818" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.740317" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.653756" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.293089" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.333477" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="53.200001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.152149" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="66.315643" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="70.229088" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="77.180756" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="88.520973" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.473122" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="101.63662" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="107.88812" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="114.83979" y="0">
−</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,191.71,66.99)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.530001">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,197.41,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="149.25999" y="7.3400002">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="157.69" y="0.0099999998">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.910317" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.250538" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.528244" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.691742" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.007198" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="66.34742" y="0.0099999998">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.374588" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="87.990112" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="92.15361" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.65493" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="101.81843" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.98193" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="112.22092" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="121.18558" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="125.34908" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="130.8504" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="137.1019" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="143.75349" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="276.70999" y="-0.23">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="280.8735" y="-0.23">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="287.125" y="-0.23">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>在哪里<年代vg height="10.75" id="M46" style="vertical-align:-0.15048pt;width:11.9125px;" version="1.1" viewbox="0 0 11.9125 10.75" width="11.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.75)">
<g transform="translate(72,-63.4)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个矩阵,这样吗<年代vg height="10.75" id="M47" style="vertical-align:-0.15048pt;width:23.1px;" version="1.1" viewbox="0 0 23.1 10.75" width="23.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.75)">
<g transform="translate(72,-63.4)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.1772022" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是可逆的。<年代vg height="11.0625" id="M48" style="vertical-align:-0.30096pt;width:39.237499px;" version="1.1" viewbox="0 0 39.237499 11.0625" width="39.237499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.990617" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.031006" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个增益矩阵后,选定和矩阵<年代vg height="13.45" id="M49" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>代表了norm-bounded参数不确定性。</p><p>gydF4y2Ba本文以下两类参数不确定性将被认为是:<年代p一个nclass="list"><span class="list-item"><span class="list-label">(一)</年代p一个n><年代p一个nclass="list-content">
<svg height="13.45" id="M50" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>norm-bounded添加剂的形式吗<年代p一个nclass="equation" id="EEq3">
<svg height="16.5375" id="M51" 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,-1,138.11,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.63019" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.79369" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.707129" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.346462" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.386848" y="0">
Δ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,196.53,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,204.88,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,227.83,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,232.7,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,240.43,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,247.39,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,270.64,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,275.51,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="198.61" y="0.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="202.7735" y="0.63">
5</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="209.02499" y="0.63">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>在哪里<年代vg height="14.2375" id="M52" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.2375" id="M53" style="vertical-align:-3.13504pt;width:17.375px;" version="1.1" viewbox="0 0 17.375 14.2375" width="17.375" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.02,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>已知矩阵和<年代vg height="14.6" id="M54" style="vertical-align:-3.13504pt;width:31.174999px;" version="1.1" viewbox="0 0 31.174999 14.6" width="31.174999" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.22,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.35,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个未知矩阵满足吗<年代p一个nclass="equation" id="eq3">
<svg height="18.7875" id="M55" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.7875" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.7875)">
<g transform="translate(72,-56.97)">
<text transform="matrix(1,0,0,-1,166.09,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,175.63,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.8099999" y="9.2200003">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,184.42,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.328438" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,206.48,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,213.43,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.716271" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.745598" y="0">
;</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="260.69" y="-0.12">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="264.85349" y="-0.12">
6</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="271.10501" y="-0.12">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span></span></span></span><span class="list"><span class="list-item"><span class="list-label">(b)</年代p一个n><年代p一个nclass="list-content">
<svg height="13.45" id="M56" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是norm-bounded乘法形式<年代p一个nclass="equation" id="EEq4">
<svg height="16.5375" id="M57" 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,-1,133.35,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.63019" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.79369" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.707129" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.346462" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.386848" y="0">
Δ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,191.77,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,200.11,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,223.07,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,227.94,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,235.67,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,242.62,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.328438" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,265.88,60.07)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,270.75,63.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.5272856" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="203.37" y="0.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="207.53349" y="0.63">
7</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="213.785" y="0.63">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>在哪里<年代vg height="14.2375" id="M58" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.2375" id="M59" style="vertical-align:-3.13504pt;width:17.375px;" version="1.1" viewbox="0 0 17.375 14.2375" width="17.375" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.02,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>已知矩阵,然后呢<年代vg height="14.6" id="M60" style="vertical-align:-3.13504pt;width:31.174999px;" version="1.1" viewbox="0 0 31.174999 14.6" width="31.174999" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.22,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.35,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个未知矩阵满足吗<年代p一个nclass="equation" id="eq4">
<svg height="18.7875" id="M61" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.7875" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.7875)">
<g transform="translate(72,-56.97)">
<text transform="matrix(1,0,0,-1,165.7,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,175.24,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.8099999" y="9.2200003">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,184.04,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,206.09,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,213.05,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.703768" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.869999" y="-0.12">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="261.07001" y="-0.12">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="265.23349" y="-0.12">
8</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="271.48499" y="-0.12">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span></span></span></span></p>
<p><span class="statement" id="rem1"><span class="statement-title"><i class="statement-title">备注3。</我></年代p一个n>从(<一个href="#EEq2">4</一个>),我们有<年代vg height="13.45" id="M62" style="vertical-align:-2.21957pt;width:52.424999px;" version="1.1" viewbox="0 0 52.424999 13.45" width="52.424999" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.5013199" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.916319" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.54315" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.583538" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。值得注意的是整型滑动面函数(<一个href="#EEq2">4</一个>)不同于现有的方法,例如,那些在[<一个href="#B10">10</一个>,<gydF4y2Ba一个href="#B11">11</一个>),因为这个词<年代vg height="13.45" id="M63" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>考虑在内。此外,这些现有的结果可以被认为是一种特殊形式的整型滑动面设计,什么时候<年代vg height="13.45" id="M64" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是零。事实上,不确定性<年代vg height="13.45" id="M65" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>不仅使设计的滑动面更放松,但也保证滑模动态有更好的鲁棒性能。<gydF4y2Babr>让<年代vg height="13.45" id="M66" style="vertical-align:-2.21957pt;width:49.5px;" version="1.1" viewbox="0 0 49.5 13.45" width="49.5" 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,-65.72,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.2264938" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.72517401" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="3.4383249" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.3517642" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.978594" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.018984" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。然后,等价控制律可以获得如下:<年代p一个nclass="equation" id="EEq5">
<svg height="20.275" id="M67" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.275" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.275)">
<g transform="translate(72,-55.78)">
<text transform="matrix(1,0,0,-1,47.19,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,53.12,57.73)">
<tspan style="font-size: 8.75px; " x="0" y="0">
e</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.8858881" y="0">
问</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,63.96,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.716271" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.907656" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.22311" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.563332" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="64.5905" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="77.206024" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="81.369522" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="85.282967" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="89.446465" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="95.685455" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="104.65011" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="108.81361" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="112.72705" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="119.66621" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="131.00644" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="135.16994" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="144.34714" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="153.54935" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,221.68,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,232.55,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.1772022" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.054571" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.819895" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.983395" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.896832" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.848499" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="57.188721" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.716248" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.879745" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="78.756393" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="85.695564" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.035782" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="106.06295" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="116.59048" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="120.75397" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="127.63062" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="133.86961" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="241.57001" y="0.090000004">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="245.73351" y="0.090000004">
9</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="251.985" y="0.090000004">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>用(<一个href="#EEq5">9</一个>)进入系统(<一个href="#EEq1">1</一个>),表示<年代vg height="18.25" id="M68" style="vertical-align:-2.21957pt;width:143.9875px;" version="1.1" viewbox="0 0 143.9875 18.25" width="143.9875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.25)">
<g transform="translate(72,-57.4)">
<g>
<path d="m -71.95,70.71 10.06,0" 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,-71.95,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.528246" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.568636" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.221672" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.561893" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.263981" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.427479" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.604683" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="80.806892" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,13.03,64.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,23.9,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.1772022" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,滑模动态和输出方程可以制定<年代p一个nclass="equation" id="EEq6">
<svg height="45.762501" id="M69" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.762501" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,45.7625)">
<g transform="translate(72,-35.39)">
<text transform="matrix(1,0,0,-1,106.22,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.6766019" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.2755461" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.439045" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.352484" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.991817" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.032206" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.195705" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.936024" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="57.276241" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="65.978333" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="78.281281" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="89.621506" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.323593" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="107.35076" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="119.96629" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.12978" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.04323" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="132.20673" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="138.45822" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="147.41037" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="151.57387" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="155.4873" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="162.43898" y="0">
+</gydF4y2Batspan>
</text>
<g>
<path d="m 280.01,70.71 10.06,0" 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,-1,280.01,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.052412" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.830238" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.993736" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.907175" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.146172" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-106.03" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-97.715508" y="20.469999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-93.55201" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-89.638565" y="20.469999">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-81.999237" y="20.469999">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-69.958847" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-61.569332" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-52.617184" y="20.469999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-48.453686" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-44.540245" y="20.469999">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-38.288746" y="20.469999">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="187.86" y="9.0900002">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="192.0235" y="9.0900002">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="198.27499" y="9.0900002">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="204.5265" y="9.0900002">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span></span></p>
<p><span class="statement" id="deff1"><span class="statement-title"><i class="statement-title">定义4。</我></年代p一个n>滑模动态(<一个href="#EEq6">10</一个>)是广义的渐近稳定<年代vg height="14.2375" id="M70" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>规范约束<年代vg height="9.9375" id="M71" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>如果下列条件。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(我)</年代p一个n><年代p一个nclass="list-content">当<年代vg height="13.45" id="M72" style="vertical-align:-2.21957pt;width:54.737499px;" version="1.1" viewbox="0 0 54.737499 13.45" width="54.737499" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6898251" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.853324" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.766764" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.393593" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.433983" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>滑模动态(<一个href="#EEq6">10</一个>)是渐近稳定的。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个nclass="list-content">滑模动态(<一个href="#EEq6">10</一个>)有一个给定的广义<年代vg height="14.2375" id="M73" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>(或<年代vg height="14.2375" id="M74" style="vertical-align:-3.13504pt;width:56.75px;" version="1.1" viewbox="0 0 56.75 14.2375" width="56.75" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.45,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-35.25,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
</text>
</g>
</g>
</svg>)抗干扰性水平;也就是说,<年代vg height="14.2375" id="M75" style="vertical-align:-3.13504pt;width:56.75px;" version="1.1" viewbox="0 0 56.75 14.2375" width="56.75" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.45,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-35.25,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
</text>
</g>
</g>
</svg>获得从扰动输入<年代vg height="13.45" id="M76" style="vertical-align:-2.21957pt;width:27.5375px;" version="1.1" viewbox="0 0 27.5375 13.45" width="27.5375" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6898251" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.853324" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.766764" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>控制输出<年代vg height="13.45" id="M77" style="vertical-align:-2.21957pt;width:23.225px;" version="1.1" viewbox="0 0 23.225 13.45" width="23.225" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.238997" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的系统(<一个href="#EEq6">10</一个>)小于给定值。这是,在新鲜感初始条件下,下列不等式:<年代p一个nclass="equation" id="EEq7">
<svg height="44.575001" id="M78" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 44.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,44.575)">
<g transform="translate(72,-36.34)">
<text transform="matrix(1,0,0,-1,167.52,51.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.863667" y="0">
u</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.115167" y="0">
p</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,160.76,41.05)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="6.7828002" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="12.77792" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,179.74,38.86)">
<tspan style="font-size: 6.25px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,183.36,41.05)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,194.93,60.69)">
<tspan style="font-size: 12.50px; " x="0" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.778066" y="0">
为</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,216.33,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="8.46">
∞</gydF4y2Batspan>
</text>
<g>
<path d="m 194.93,54.68 30,0" 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,-1,195.07,40.53)">
<tspan style="font-size: 12.50px; " x="0" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.228893" y="0">
为</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,219.92,45.88)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.2200003">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,229.6,51.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,247.99,56.56)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,252.86,51.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="215.00999" y="0.51999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="219.17349" y="0.51999998">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="225.425" y="0.51999998">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="231.6765" y="0.51999998">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>在哪里<年代p一个nclass="equation" id="eq5">
<svg height="38.325001" id="M79" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.325001" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,38.325)">
<g transform="translate(72,-41.34)">
<text transform="matrix(1,0,0,-1,61.33,54.15)">
<tspan style="font-size: 12.50px; " x="0" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.228893" y="0">
为</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,86.18,59.5)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.2200003">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,94.53,54.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.04" y="7.6999998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,113.57,68.19)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.530001">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,124.25,54.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,133.94,59.16)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,142.74,54.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.093761" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.257259" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.1707" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.409695" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.061291" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.974731" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="76.118263" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="82.657333" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="88.896332" y="0">
为</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,240.26,59.5)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="8.4700003">
∞</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,252.34,54.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.891554" y="0">
u</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.143053" y="0">
p</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,272.73,43.94)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,285.91,51.65)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1900001" y="-2.51">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,299.34,59.16)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,308.14,54.16)">
<tspan style="font-size: 12.50px; " x="34.880001" y="2.51">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.16" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.642933" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.806433" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.719872" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="159.73" y="0.62">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="163.89349" y="0.62">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.145" y="0.62">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="176.3965" y="0.62">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span></span></span></span></span></p>
<p><span class="statement" id="thm1"><span class="statement-title">定理5。</年代p一个n><我>考虑到系统(<一个href="#EEq6">10</一个>)和一个给定的常数<年代vg height="13.6125" id="M80" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.8148546" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.855244" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。如果存在矩阵<年代vg height="11.0625" id="M81" style="vertical-align:-0.30096pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 11.0625" width="36.612499" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.890113" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.930502" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="10.325" id="M82" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样下面的矩阵不等式都是真的</我><年代p一个nclass="equation" id="EEq8">
<svg height="167.625" id="M83" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 167.625" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,167.625)">
<g transform="translate(72,62.1)">
<text transform="matrix(1,0,0,-1,50.49,43.82)">
<tspan style="font-size: 12.50px; " x="27.040001" y="-13.08">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.040001" y="-2.23">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.040001" y="8.6099997">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.040001" y="19.4">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
Θ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.0036" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.669998" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.047729" y="-10.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.211227" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.951546" y="-10.63">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.304268" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="80.006355" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="92.309311" y="-10.63">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="103.64953" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="112.35162" y="-10.63">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="121.37878" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="133.99431" y="-10.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="138.15781" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="142.07124" y="-10.63">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="146.23476" y="-10.63">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="153.17392" y="-10.63">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="164.51413" y="-10.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="168.67763" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="180.41795" y="-10.63">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="191.77068" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="200.47276" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="212.77571" y="-10.63">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="224.11594" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="232.81802" y="-10.63">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="241.84518" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="254.46072" y="-10.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="258.62421" y="-10.63">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="262.53766" y="-10.63">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="266.70114" y="-10.63">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,321.36,59.62)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,328.07,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.278666" y="0">
</gydF4y2Batspan>
</text>
<g>
<path d="m 352.65,65.5 10.07,0" 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,-1,352.65,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.07" y="-2.45">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.07" y="8.3999996">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.07" y="19.24">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.07" y="30.030001">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-178.12" y="81.529999">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-178.12" y="92.379997">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-178.12" y="103.23">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-178.12" y="114.02">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-145.64999" y="25.01">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-7.46" y="25.01">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="1.104555" y="25.01">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-287.14999" y="50.02">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-275.1221" y="50.02">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-268.87061" y="50.02">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="115.22" y="23.129999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="119.3835" y="23.129999">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="125.635" y="23.129999">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="131.88651" y="23.129999">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-172.49001" y="83.989998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.09857" y="83.989998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,205.95,-24.54)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,181.54,-54.55)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.890833" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,201.79,-49.54)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,206.66,-54.55)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1300001" y="-27.469999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1300001" y="-16.620001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1300001" y="-5.77">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1300001" y="5.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.23" y="-14.38">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.257887" y="-14.38">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.509384" y="-14.38">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="261.20999" y="-14.38">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="265.3735" y="-14.38">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="271.625" y="-14.38">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="277.8765" y="-14.38">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><i><span class="displayed-label" id="EEq9"></span>然后滑模动态(<一个href="#EEq6">10</一个>)是广义的渐近稳定<年代vg height="14.2375" id="M85" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>规范约束<年代vg height="9.9375" id="M86" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></p>
<p><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>考虑下面的李雅普诺夫函数的候选人:<年代p一个nclass="equation" id="EEq10">
<svg height="18.2125" id="M87" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.2125" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.2125)">
<g transform="translate(72,-57.43)">
<text transform="matrix(1,0,0,-1,155.51,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,162.7,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,169.66,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.703768" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,204.28,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,213.08,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.742718" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.707369" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.870869" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.784306" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.035805" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="254.78999" y="-0.34999999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="258.95349" y="-0.34999999">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="265.20499" y="-0.34999999">
5</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="271.45651" y="-0.34999999">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>的时间导数<年代vg height="14.6" id="M88" style="vertical-align:-3.13504pt;width:30.5px;" version="1.1" viewbox="0 0 30.5 14.6" width="30.5" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.76,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.89,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>沿着轨迹系统(<一个href="#EEq6">10</一个>),<gydF4y2Ba年代vg height="13.45" id="M89" style="vertical-align:-2.21957pt;width:54.737499px;" version="1.1" viewbox="0 0 54.737499 13.45" width="54.737499" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6898251" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.853324" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.766764" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.393593" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.433983" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是由<年代p一个nclass="equation" id="EEq11">
<svg height="49.974998" id="M90" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.974998" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,49.975)">
<g transform="translate(72,-32.02)">
<text transform="matrix(1,0,0,-1,101.38,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-7.8699999" y="2.54">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,100.69,57.93)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,107.65,61.07)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0834389" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.710269" y="0.0099999998">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.750658" y="0.0099999998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,142.28,66.06)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,151.08,61.07)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.32" y="2.52">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0734386" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.110001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.48773" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.65123" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.391544" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="57.74427" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="66.446358" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="78.749313" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.089531" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.791618" y="0.0099999998">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="107.81879" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="120.43431" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.59781" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.51125" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="132.67474" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.96" y="24.43">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.524555" y="24.43">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.688053" y="24.43">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.428371" y="24.43">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.768593" y="24.43">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.47068" y="24.43">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="64.773628" y="24.43">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="76.113853" y="24.43">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="84.815941" y="24.43">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="93.843109" y="24.43">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="106.45863" y="24.43">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="110.62213" y="24.43">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="114.53557" y="24.43">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="118.69907" y="24.43">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,273.95,41.81)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,280.66,36.64)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3000002" y="2.52">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.18" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.132149" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.295647" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.209087" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.448082" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="187.21001" y="-12.25">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="191.3735" y="-12.25">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="197.625" y="-12.25">
6</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="203.8765" y="-12.25">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><br>从(<一个href="#EEq8">13</一个>),<gydF4y2Ba年代vg height="11.0625" id="M91" style="vertical-align:-0.30096pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 11.0625" width="38.612499" 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">
Θ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.490497" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.530886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>意味着<年代vg height="16.5" id="M92" style="vertical-align:-2.21957pt;width:330.08749px;" version="1.1" viewbox="0 0 330.08749 16.5" width="330.08749" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.4267821" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.590281" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.330599" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.670818" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.372906" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.675858" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.016083" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.71817" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="84.745331" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="94.272621" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.436119" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="102.34956" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="106.51305" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="113.46472" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.80495" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.96844" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="140.70876" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="152.04898" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="160.75107" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="173.06653" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="184.40675" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="193.10884" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="202.136" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="211.66328" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="215.82678" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="219.74022" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="223.90372" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,156.12,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,162.83,61.07)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.902616" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.930502" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,那么我们就有<年代p一个nclass="equation" id="EEq12">
<svg height="17.7125" id="M93" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.7125" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.7125)">
<g transform="translate(72,-57.83)">
<text transform="matrix(1,0,0,-1,190.61,64.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-7.8699999" y="2.53">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,189.93,58.51)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,196.88,61.64)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.716271" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.995659" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="270.98999" y="-0.15000001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="275.1535" y="-0.15000001">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="281.405" y="-0.15000001">
7</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="287.65649" y="-0.15000001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>这意味着滑模动态(<一个href="#EEq6">10</一个>)是渐近稳定的,当<年代vg height="13.45" id="M94" style="vertical-align:-2.21957pt;width:54.737499px;" version="1.1" viewbox="0 0 54.737499 13.45" width="54.737499" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6898251" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.853324" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.766764" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.393593" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.433983" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。<gydF4y2Babr>为了构造广义<年代vg height="14.2375" id="M95" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>(<年代vg height="14.2375" id="M96" style="vertical-align:-3.13504pt;width:56.75px;" version="1.1" viewbox="0 0 56.75 14.2375" width="56.75" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.45,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-35.25,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
</text>
</g>
</g>
</svg>)性能指标,我们假设新鲜感初始条件,然后<年代vg height="14.75" id="M97" style="vertical-align:-3.25793pt;width:77.849998px;" version="1.1" viewbox="0 0 77.849998 14.75" width="77.849998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.75)">
<g transform="translate(72,-60.2)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.76,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.89,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.240437" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-45.15,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.7393761" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.7344961" y="0">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.06,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。现在,我们考虑下面的成本性能:<年代p一个nclass="equation" id="EEq13">
<svg height="38.387501" id="M98" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,38.3875)">
<g transform="translate(72,-41.29)">
<text transform="matrix(1,0,0,-1,131.95,52.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.227454" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.255341" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,161.41,49.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,168.36,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.370001" y="7.71">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0834389" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.010101" y="0.0099999998">
−</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,201.73,66.99)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.530001">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,207.43,52.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,217.12,57.96)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,225.92,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6613197" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.91282" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.678143" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.841642" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.34296" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.594463" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.246059" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.747379" y="0.0099999998">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="241.95" y="-0.55000001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="246.11349" y="-0.55000001">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="252.36501" y="-0.55000001">
8</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="258.61649" y="-0.55000001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>对于任何非零<年代vg height="14.6" id="M99" style="vertical-align:-3.13504pt;width:103.2875px;" version="1.1" viewbox="0 0 103.2875 14.6" width="103.2875" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6898251" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.853324" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.766764" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.393593" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.433983" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-25.66,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-20.78,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">
∞</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.194025" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,我们有<年代p一个nclass="equation" id="EEq14">
<svg height="87.862503" id="M100" 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,-1,127.18,52.96)">
<tspan style="font-size: 12.50px; " x="23.77" y="7.6999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.727814" y="0">
=</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,157.95,66.99)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.530001">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,163.66,50.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.66" y="-5.0500002">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.7800002" y="-2.51">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,175.63,49.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,182.59,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.67132" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.597982" y="0.0099999998">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.950706" y="0.0099999998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,220.23,57.96)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,229.03,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.509998" y="2.52">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-90.120003" y="39.59">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-78.080002" y="47.279999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6613197" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.900317" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.678143" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.841642" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.34296" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.380001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.031597" y="0.0099999998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,157.95,27.41)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.52">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,163.66,13.38)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,169.69,18.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,176.41,13.38)">
<tspan style="font-size: 12.50px; " x="0" y="0">
Θ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.141613" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.793209" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.294529" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="291.45999" y="-20.35">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="295.6235" y="-20.35">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="301.875" y="-20.35">
9</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="308.1265" y="-20.35">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>在哪里<年代vg height="16.375" id="M101" style="vertical-align:-2.29482pt;width:117.925px;" version="1.1" viewbox="0 0 117.925 16.375" width="117.925" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.375)">
<g transform="translate(72,-58.9)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.5022802" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.542669" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.706167" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-39.36,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.65,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.828318" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-9.13,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-2.42,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.828318" y="0">
]</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,15.57,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。<gydF4y2Babr>从(<一个href="#EEq8">13</一个>),我们得到<年代p一个nclass="equation" id="EEq15">
<svg height="38.387501" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,38.3875)">
<g transform="translate(72,-41.29)">
<text transform="matrix(1,0,0,-1,121.07,52.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.214951" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.255341" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,150.52,49.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,157.48,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.360001" y="7.71">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0834389" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.010101" y="0.0099999998">
−</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,190.85,66.99)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.530001">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,196.55,52.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,206.24,57.96)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,215.04,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6613197" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.900317" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.678143" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.841642" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.34296" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.594463" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.246059" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.223213" y="0.0099999998">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.251099" y="0.0099999998">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="77.502602" y="0.0099999998">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="252.83" y="-0.55000001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="256.9935" y="-0.55000001">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="263.245" y="-0.55000001">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="269.49649" y="-0.55000001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>方程(<一个href="#EEq15">20.</一个>)导致<年代p一个nclass="equation" id="EEq16">
<svg height="38.387501" id="M103" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,38.3875)">
<g transform="translate(72,-41.29)">
<text transform="matrix(1,0,0,-1,105.32,52.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,112.2,57.96)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,120.99,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0834389" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.322436" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.749218" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.713869" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.877369" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.790806" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.417637" y="0.0099999998">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.458027" y="0.0099999998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,186.65,49.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,193.61,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.75" y="7.71">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0734386" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.700269" y="0.0099999998">
<</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,228.36,66.99)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.530001">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,234.07,52.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,243.76,57.96)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,252.55,52.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.67132" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.910317" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.67564" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.83914" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.340458" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.591961" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.243553" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.744877" y="0.0099999998">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="215.32001" y="-0.55000001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="219.48351" y="-0.55000001">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="225.735" y="-0.55000001">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="231.9865" y="-0.55000001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>(<一个href="#EEq9">14</一个>),由引理<一个href="#lem1">1</一个>,我们有<年代p一个nclass="equation" id="EEq17">
<svg height="18.4625" id="M104" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.4625)">
<g transform="translate(72,-57.23)">
<text transform="matrix(1,0,0,-1,178.11,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,187.5,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,194.21,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.852844" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.893232" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,224.46,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,229.34,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="238.53" y="-0.46000001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="242.6935" y="-0.46000001">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="248.94499" y="-0.46000001">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="255.1965" y="-0.46000001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>导致<年代p一个nclass="equation" id="EEq18">
<svg height="145.2" id="M105" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 145.2" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,145.2)">
<g transform="translate(72,44.16)">
<text transform="matrix(1,0,0,-1,121.48,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,127.72,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,136.51,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.642933" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.806433" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.719872" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.359203" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.399593" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,193.79,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,202.58,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.328438" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,226.3,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,233.01,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.389513" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.341661" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.505159" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.418598" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-58.139999" y="23.629999">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-46.099609" y="23.629999">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,193.26,42.6)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,198.14,37.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,205.01,42.6)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,213.81,37.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.742718" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.707369" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.870869" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.784306" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-38.939999" y="31.709999">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-26.899611" y="31.709999">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,193.26,10.89)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,200.22,-1.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,207.22,19.92)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.530001">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,212.93,5.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,222.62,10.89)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,231.42,5.9)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.903816" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.681643" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.84514" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.346462" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.585457" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.237053" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-56.549999" y="38.389999">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-44.509609" y="38.389999">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,193.26,-27.49)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,200.22,-40.18)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,207.22,-18.46)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.25" y="25.52">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,217.91,-32.49)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,227.6,-27.49)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,236.4,-32.48)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.903816" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.681643" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.84514" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.346462" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.585457" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.237053" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.738373" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="231.47" y="-43.279999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="235.6335" y="-43.279999">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="241.88499" y="-43.279999">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="248.13651" y="-43.279999">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>对于任何时间<年代vg height="12.3" id="M106" style="vertical-align:-1.29163pt;width:32.224998px;" version="1.1" viewbox="0 0 32.224998 12.3" width="32.224998" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.37677" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.417158" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,最大的价值<年代vg height="16.2875" id="M107" style="vertical-align:-2.21957pt;width:54.712502px;" version="1.1" viewbox="0 0 54.712502 16.2875" width="54.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2875)">
<g transform="translate(72,-58.97)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.71,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.240437" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.479433" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.642933" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.556372" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,我们有<年代p一个nclass="equation" id="EEq19">
<svg height="19.0375" id="M108" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.0375" width="700.9375" 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,-1,156.42,60.69)">
<tspan style="font-size: 12.50px; " x="0" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.778066" y="0">
为</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,177.82,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="8.46">
∞</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,189.89,60.69)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,208.28,65.7)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,213.16,60.69)">
<tspan style="font-size: 12.50px; " x="30.549999" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.309999" y="-0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.473499" y="-0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.386938" y="-0.0099999998">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,252.33,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.21">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,257.21,60.69)">
<tspan style="font-size: 12.50px; " x="0" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="210.66" y="-0.56999999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="214.8235" y="-0.56999999">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="221.075" y="-0.56999999">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="227.32649" y="-0.56999999">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><br>完成证明。</年代p一个n></p><p>滑模动态(<一个href="#EEq6">10</一个>加法和乘法的不确定性,下面的定理给出一些充分条件,保证滑模动态渐近稳定广义<年代vg height="14.2375" id="M109" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>规范约束<年代vg height="9.9375" id="M110" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p><年代p一个nclass="statement" id="thm2"><span class="statement-title">定理6。</年代p一个n><我>考虑到系统(<一个href="#EEq6">10</一个>),不确定性<年代vg height="13.45" id="M111" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在(<一个href="#EEq3">5</一个>),一个给定的常数<年代vg height="13.6125" id="M112" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.8148546" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.855244" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。如果存在矩阵<年代vg height="11.0625" id="M113" style="vertical-align:-0.30096pt;width:39.674999px;" version="1.1" viewbox="0 0 39.674999 11.0625" width="39.674999" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.340701" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.38109" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="10.325" id="M114" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和一个标量<年代vg height="14.6" id="M115" style="vertical-align:-3.13504pt;width:40.987499px;" version="1.1" viewbox="0 0 40.987499 14.6" width="40.987499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.55,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样下面的线性矩阵不等式(lmi)是正确的</我><年代p一个nclass="equation" id="EEq20">
<svg height="167.625" id="M116" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 167.625" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,167.625)">
<g transform="translate(72,62.1)">
<text transform="matrix(1,0,0,-1,55.13,56.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="11.5">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="23.01">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="34.52">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="46.02">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="57.470001">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.6199999" y="2.4400001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.584651" y="2.4400001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.237686" y="2.4400001">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.577908" y="2.4400001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.455276" y="2.4400001">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,112.56,59.5)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,122.05,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.042309" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.50708" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.847301" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,172.1,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,178.81,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,188.01,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,197.5,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,214.9,51.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,219.77,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.7020884" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,239.39,51.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,244.26,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,256.3,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.12" y="9.2200003">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,263.01,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,272.22,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<g>
<path d="m 287.72,65.5 10.06,0" 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,-1,287.72,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.029566" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.906937" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,326.31,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,166.57,29.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="118.34" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.90456" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="150.18513" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="25.01">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="122.91" y="25.01">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="140.0016" y="25.01">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="148.56616" y="25.01">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,321.19,1.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,326.07,4.43)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-52.459999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-40.959999">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-29.450001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-17.940001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-6.4400001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="5.0100002">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="31.51">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="42.360001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="53.209999">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="64">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.219999" y="-26.889999">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.247887" y="-26.889999">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.499386" y="-26.889999">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="141.8" y="-26.889999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="145.9635" y="-26.889999">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="152.215" y="-26.889999">
5</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.46649" y="-26.889999">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-150.39" y="33.970001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-133.78601" y="33.970001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-123.90865" y="33.970001">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,211.55,-24.54)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,177.73,-54.55)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.366907" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,202.45,-49.54)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,207.33,-54.55)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="-27.469999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="-16.620001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="-5.77">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="5.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.040001" y="-14.38">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.067886" y="-14.38">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.319386" y="-14.38">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="260.54001" y="-14.38">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="264.70349" y="-14.38">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="270.95499" y="-14.38">
6</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="277.20651" y="-14.38">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><i><span class="displayed-label" id="EEq21"></span>然后滑模动态(<一个href="#EEq6">10</一个>)是广义的渐近稳定<年代vg height="14.2375" id="M118" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>规范约束<年代vg height="9.9375" id="M119" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。此外,增益矩阵<年代vg height="10.325" id="M120" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>被选为<年代vg height="13.775" id="M121" style="vertical-align:-0.0pt;width:66.650002px;" version="1.1" viewbox="0 0 66.650002 13.775" width="66.650002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.990617" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.031006" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.720112" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-29.6,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></p>
<p><span class="statement" id="proof2"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>预处理和自右乘(<一个href="#EEq8">13</一个>)和(<一个href="#EEq9">14</一个>)<gydF4y2Ba年代vg height="14.2" id="M122" style="vertical-align:-2.73372pt;width:73.612503px;" version="1.1" viewbox="0 0 73.612503 14.2" width="73.612503" 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">
d</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">
一个</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.278666" y="0">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.693665" y="0">
{</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.695105" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.572475" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.773724" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.775162" y="0">
}</gydF4y2Batspan>
</text>
</g>
</g>
</svg>与<年代vg height="13.775" id="M123" style="vertical-align:-0.0pt;width:57.075001px;" version="1.1" viewbox="0 0 57.075001 13.775" width="57.075001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.340701" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.38109" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-37.26,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们分别<年代p一个nclass="equation" id="EEq22">
<svg height="62.637501" id="M124" 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,-1,51.41,56.9)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="10.85">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="21.690001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="32.48">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.6300001" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.793499" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.533815" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.874039" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.576126" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="53.879078" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="65.219299" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="73.921387" y="2.45">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="82.948555" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="95.564079" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="99.727577" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="103.64101" y="2.45">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="107.80452" y="2.45">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="114.05602" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.70905" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="138.04927" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="148.67682" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="152.84032" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="164.58064" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="175.93336" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="184.63545" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="196.9384" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="208.27863" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="216.98071" y="2.45">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="226.00787" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="238.6234" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="242.78691" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="246.70035" y="2.45">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="250.86385" y="2.45">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,306.44,59.62)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<g>
<path d="m 321.95,65.5 10.06,0" 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,-1,321.95,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.87" y="-2.45">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.87" y="8.3999996">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.87" y="19.24">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.87" y="30.030001">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-140.12" y="25.01">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.8199999" y="25.01">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.744555" y="25.01">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.969999" y="10.63">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.010387" y="10.63">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.26189" y="10.63">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="145.92" y="10.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="150.0835" y="10.63">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="156.33499" y="10.63">
7</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="162.5865" y="10.63">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>和(<一个href="#EEq21">26</一个>)。<gydF4y2Babr>从(<一个href="#EEq22">27</一个>),我们可以获得<年代p一个nclass="equation" id="EEq23">
<svg height="139.39999" id="M125" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 139.39999" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,139.4)">
<g transform="translate(72,39.52)">
<text transform="matrix(1,0,0,-1,53.07,56.9)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="10.85">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="21.690001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="32.48">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.6199999" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7834988" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.523815" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.864037" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.566124" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.093651" y="2.45">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.34515" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="70.998184" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="82.338409" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="92.965958" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.129456" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="108.86977" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="120.2225" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.92459" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.45212" y="2.45">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,196.69,59.62)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<g>
<path d="m 212.19,65.5 10.07,0" 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,-1,212.19,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="-2.45">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="8.3999996">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="19.24">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="30.030001">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.290001" y="10.63">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.630001" y="-2.45">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.630001" y="8.3999996">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.630001" y="19.24">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.630001" y="30.030001">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-84.410004" y="25.01">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.8099999" y="25.01">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.7545552" y="25.01">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.25" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.952087" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,270.06,51.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,259.56,29.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.38" y="-27.459999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.38" y="-16.610001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.38" y="-5.77">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.38" y="5.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.09" y="-14.38">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,290.37,40.69)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,297.33,43.82)">
<tspan style="font-size: 12.50px; " x="14.33" y="4.9200001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.059999" y="1.88">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,326.32,38.82)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,337.17,41.94)">
<tspan style="font-size: 12.50px; " x="22.860001" y="3.04">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-263.48001" y="59.529999">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-252.14" y="46.450001">
⎛</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-252.14" y="57.299999">
⎜</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-252.14" y="68.150002">
⎜</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-252.14" y="78.93">
⎝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-246.50999" y="46.450001">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-246.50999" y="57.299999">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-246.50999" y="68.150002">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-246.50999" y="78.93">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.603985" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-240.89" y="48.91">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-232.18791" y="48.91">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,115.9,-10.09)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,105.4,-31.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-27.459999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-16.610001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-5.7600002">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="5.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.08" y="-14.38">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,136.21,-20.72)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,143.17,-17.59)">
<tspan style="font-size: 12.50px; " x="14.32" y="4.9200001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.059999" y="1.88">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,172.16,-22.59)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,183.01,-19.47)">
<tspan style="font-size: 12.50px; " x="22.860001" y="3.04">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.6" y="-14.96">
⎞</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.6" y="-4.1100001">
⎟</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.6" y="6.7399998">
⎟</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.6" y="17.52">
⎠</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.603985" y="0">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,217.23,7.26)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,227.42,-17.59)">
<tspan style="font-size: 12.50px; " x="0" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="240.45" y="-30.700001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="244.61349" y="-30.700001">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="250.86501" y="-30.700001">
8</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="257.11649" y="-30.700001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>从引理<一个href="#lem2">2</一个>,(<gydF4y2Ba一个href="#EEq23">28</一个>)当且仅当存在一个标量<年代vg height="14.6" id="M126" style="vertical-align:-3.13504pt;width:40.987499px;" version="1.1" viewbox="0 0 40.987499 14.6" width="40.987499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.55,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样,下面的不平等是适用的:<年代p一个nclass="equation" id="EEq24">
<svg height="139.39999" id="M127" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 139.39999" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,139.4)">
<g transform="translate(72,39.52)">
<text transform="matrix(1,0,0,-1,66.89,54.47)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="10.85">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="21.700001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="32.48">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.6300001" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.793499" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.533815" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.874039" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.576126" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.103649" y="2.45">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.355152" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.008186" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="82.348412" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="92.97596" y="2.45">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.139458" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="108.87978" y="2.45">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="120.2325" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.93459" y="2.45">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.46211" y="2.45">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,210.52,57.19)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<g>
<path d="m 226.02,63.07 10.07,0" 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,-1,226.02,52.01)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="-2.46">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="8.3900003">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="19.24">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.88" y="30.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-84.410004" y="25">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.8099999" y="25">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.7545552" y="25">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.280001" y="10.62">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.62022" y="10.62">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,264.7,38.26)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,271.66,54.47)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="10.85">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="21.700001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="32.48">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.6199999" y="2.46">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.322088" y="2.46">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,296.9,48.89)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,286.4,27.01)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-27.459999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-16.610001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-5.7600002">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="5.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.08" y="-27.459999">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.08" y="-16.610001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.08" y="-5.7600002">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.08" y="5.02">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.709999" y="-25">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.412086" y="-25">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,334.73,48.89)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,324.23,27.01)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-27.459999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-16.610001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="-5.7600002">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.37" y="5.02">
⎦</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,345.23,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,87.51,-17.59)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.88" y="-7.25">
1</gydF4y2Batspan>
</text>
<g>
<path d="m 100.05,-14.47 10.93,0" 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,-1,100.05,-26.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,106.1,-29.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
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<text transform="matrix(1,0,0,-1,114.26,-4.51)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="10.85">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="21.700001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="32.48">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.6199999" y="2.46">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.49737" y="2.46">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,139.44,-1.96)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003">
1</gydF4y2Batspan>
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<text transform="matrix(1,0,0,-1,129.89,-31.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.26" y="-27.459999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.26" y="-16.610001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.26" y="-5.7600002">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.26" y="5.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.969999" y="-9.46">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.709999" y="-12.5">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,168.53,-22.59)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,179.38,-19.47)">
<tspan style="font-size: 12.50px; " x="22.860001" y="3.04">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.603985" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.07" y="-1.88">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.097885" y="-1.88">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.349384" y="-1.88">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="288.48999" y="-32.580002">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="292.6535" y="-32.580002">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="298.905" y="-32.580002">
9</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="305.15649" y="-32.580002">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>根据引理,<一个href="#lem1">1</一个>相当于(<一个href="#EEq20">25</一个>)。<gydF4y2Babr>完成证明。</年代p一个n></p><p><span class="statement" id="thm3"><span class="statement-title">定理7。</年代p一个n><我>考虑到系统(<一个href="#EEq6">10</一个>),不确定性<年代vg height="13.45" id="M128" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在(<一个href="#EEq4">7</一个>),一个给定的常数<年代vg height="13.6125" id="M129" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.8148546" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.855244" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。如果存在矩阵<年代vg height="11.0625" id="M130" style="vertical-align:-0.30096pt;width:39.674999px;" version="1.1" viewbox="0 0 39.674999 11.0625" width="39.674999" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.340701" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.38109" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="10.325" id="M131" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和标量<年代vg height="14.6" id="M132" style="vertical-align:-3.13504pt;width:40.987499px;" version="1.1" viewbox="0 0 40.987499 14.6" width="40.987499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.55,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样下面的线性矩阵不等式(lmi)是正确的</我><年代p一个nclass="equation" id="EEq25">
<svg height="167.625" id="M133" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 167.625" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,167.625)">
<g transform="translate(72,62.1)">
<text transform="matrix(1,0,0,-1,55.13,56.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="11.5">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="23.01">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="34.52">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="46.02">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="57.470001">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.6199999" y="2.4400001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.584651" y="2.4400001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.237686" y="2.4400001">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.577908" y="2.4400001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.455276" y="2.4400001">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,112.56,59.5)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,122.05,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.042309" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.50708" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.847301" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,172.1,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,178.81,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,188.01,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,197.5,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,214.9,51.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,219.77,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.7020884" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,239.39,51.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,244.26,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,256.3,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.12" y="9.2200003">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,263.01,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,272.22,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<g>
<path d="m 287.72,65.5 10.06,0" 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,-1,287.72,54.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.617447" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.306553" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,324.71,59.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,166.57,29.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="118.34" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.90456" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="150.18513" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="25.01">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="122.91" y="25.01">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="140.0016" y="25.01">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="148.56616" y="25.01">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,321.19,1.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,326.07,4.43)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-52.459999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-40.959999">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-29.450001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-17.940001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="-6.4400001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1199999" y="5.0100002">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="31.51">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="42.360001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="53.209999">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-156.02" y="64">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.219999" y="-26.889999">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.247887" y="-26.889999">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.499386" y="-26.889999">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="141.8" y="-26.889999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="145.9635" y="-26.889999">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="152.215" y="-26.889999">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.46649" y="-26.889999">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-150.39" y="33.970001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-133.78601" y="33.970001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-123.90865" y="33.970001">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,211.55,-24.54)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,177.73,-54.55)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.366907" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,202.45,-49.54)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,207.33,-54.55)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="-27.469999">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="-16.620001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="-5.77">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.94" y="5.02">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.040001" y="-14.38">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.067886" y="-14.38">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.319386" y="-14.38">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="260.54001" y="-14.38">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="264.70349" y="-14.38">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="270.95499" y="-14.38">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="277.20651" y="-14.38">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><i><span class="displayed-label" id="EEq26"></span>然后滑模动态(<一个href="#EEq6">10</一个>)是广义的渐近稳定<年代vg height="14.2375" id="M135" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>规范约束<年代vg height="9.9375" id="M136" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。此外,增益矩阵<年代vg height="10.325" id="M137" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>被选为<年代vg height="13.775" id="M138" style="vertical-align:-0.0pt;width:66.650002px;" version="1.1" viewbox="0 0 66.650002 13.775" width="66.650002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.990617" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.031006" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.720112" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-29.6,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></p>
<p><span class="statement" id="proof3"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>类似于定理证明<一个href="#thm2">6</一个>,省略了。</年代p一个n></p><h5 id="sec3.2">3.2。滑模控制器设计</gydF4y2Bah5>
<p>输入<年代vg height="13.45" id="M139" style="vertical-align:-2.21957pt;width:22.8375px;" version="1.1" viewbox="0 0 22.8375 13.45" width="22.8375" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.9264221" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.089921" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.00336" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在系统(<一个href="#EEq1">1</一个>)应该适当的设计状态<年代vg height="13.45" id="M140" style="vertical-align:-2.21957pt;width:24.025px;" version="1.1" viewbox="0 0 24.025 13.45" width="24.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.8766499" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.953588" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在系统(<一个href="#EEq1">1</一个>)到达滑动面<年代vg height="13.45" id="M141" style="vertical-align:-2.21957pt;width:49.5px;" version="1.1" viewbox="0 0 49.5 13.45" width="49.5" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.5013199" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.578258" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.205088" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.245476" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在一个有限的时间。非脆弱滑模控制器<年代vg height="13.45" id="M142" style="vertical-align:-2.21957pt;width:22.8375px;" version="1.1" viewbox="0 0 22.8375 13.45" width="22.8375" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.9264221" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.089921" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.00336" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>如下:<年代p一个nclass="equation" id="EEq27">
<svg height="49.112499" id="M143" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.112499" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,49.1125)">
<g transform="translate(72,-32.71)">
<text transform="matrix(1,0,0,-1,44.14,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0019197" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.165419" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.078857" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.718191" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.758579" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.922077" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.225033" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.56525" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="72.592415" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="85.207947" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="89.371445" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="93.284882" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.44838" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="103.68738" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="112.65203" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="116.81553" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="120.72897" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="127.66814" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.00835" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="149.53587" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="153.69939" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="160.57603" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="167.5152" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="178.86792" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="183.03142" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="192.20862" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="201.41083" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,249.72,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,77.13,37.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">
×</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.86" y="2.51">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="285.48001" y="2.51">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="292.35999" y="7.1054274e-015">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.65" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.701693" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.290001" y="-0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.453499" y="-0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.36694" y="-0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.306103" y="-0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.646324" y="-0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.82" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="69.35907" y="0">
G</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="78.386238" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="88.438644" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="99.841385" y="0">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="106.19291" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="112.73198" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.52" y="-0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.6835" y="-0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="132.59694" y="-0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="136.75999" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="148.15024" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="159.49045" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="166.02953" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="175.20673" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="184.40894" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="195.81168" y="0">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="202.16319" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="211.22787" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="222.56808" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="229.55" y="-0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="235.789" y="-0.0099999998">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="240.65266" y="-0.0099999998">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="246.90416" y="-0.0099999998">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="257.33167" y="-0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="261.49518" y="-0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="269.07199" y="-0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="273.23547" y="-0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="277.14893" y="-0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="281.31241" y="-0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="390.73999" y="-11.91">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="394.9035" y="-11.91">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="401.155" y="-11.91">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="407.40649" y="-11.91">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>在哪里<年代vg height="17.512501" id="M144" style="vertical-align:-3.20526pt;width:301.8125px;" version="1.1" viewbox="0 0 301.8125 17.512501" width="301.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.5125)">
<g transform="translate(72,-57.99)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.863667" y="0">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.115167" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.530167" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.693665" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.194984" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.358482" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.271923" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.435421" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.074757" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.102642" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.266144" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="72.129807" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.605644" y="0">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="81.85714" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="92.284645" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="96.448143" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,30,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,34.88,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.364747" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.228414" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.704248" y="0">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.955748" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.370747" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.534245" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,78.93,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,83.8,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.364747" y="0">
…</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.955748" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.156996" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.020664" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.496498" y="0">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.747997" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="54.175499" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.338997" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,147.65,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,154.36,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
]</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,162.68,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="11.0625" id="M145" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.515023" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.555412" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="13.55" id="M146" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.440005" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.480394" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p><年代p一个nclass="statement" id="thm4"><span class="statement-title">定理8。</年代p一个n><我>考虑到系统(<一个href="#EEq1">1</一个>)。如果输入<年代vg height="13.45" id="M147" style="vertical-align:-2.21957pt;width:22.8375px;" version="1.1" viewbox="0 0 22.8375 13.45" width="22.8375" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.9264221" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.089921" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.00336" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作为(<一个href="#EEq27">32</一个>),那么系统的轨迹(<一个href="#EEq1">1</一个>)收敛于滑动面<年代vg height="13.45" id="M148" style="vertical-align:-2.21957pt;width:49.5px;" version="1.1" viewbox="0 0 49.5 13.45" width="49.5" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.5013199" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.578258" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.205088" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.245476" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在一个有限的时间。</我></年代p一个n></p>
<p><span class="statement" id="proof4"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>考虑一个李雅普诺夫函数的候选人如下:<年代p一个nclass="equation" id="EEq28">
<svg height="30.700001" id="M149" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,30.7)">
<g transform="translate(72,-47.44)">
<text transform="matrix(1,0,0,-1,156.28,56.25)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,163.47,53.12)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,170.42,56.25)">
<tspan style="font-size: 12.50px; " x="28.950001" y="-7.25">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.716271" y="0">
=</gydF4y2Batspan>
</text>
<g>
<path d="m 199.37,59.37 6.25,0" 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,-1,199.37,47.49)">
<tspan style="font-size: 12.50px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,212.32,61.25)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,221.12,56.25)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.315935" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.892754" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.056252" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.96969" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.221191" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="246.75" y="-0.34999999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="250.9135" y="-0.34999999">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="257.16501" y="-0.34999999">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="263.4165" y="-0.34999999">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>计算的时间导数<年代vg height="14.6" id="M150" style="vertical-align:-3.13504pt;width:30.5px;" version="1.1" viewbox="0 0 30.5 14.6" width="30.5" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.76,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.89,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>沿着轨迹的系统(<一个href="#EEq1">1</一个>),我们有<年代p一个nclass="equation" id="EEq29">
<svg height="43.799999" id="M151" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.799999" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,43.8)">
<g transform="translate(72,-36.96)">
<text transform="matrix(1,0,0,-1,90.63,63.77)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-7.8699999" y="2.54">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,89.95,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,96.9,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.716271" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,130.16,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,138.95,61.24)">
<tspan style="font-size: 12.50px; " x="14.33" y="0.039999999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="155.94" y="20.52">
]</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="162.19" y="20.48">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.49" y="0.0099999998">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.054556" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.231758" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.509464" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.672962" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.975914" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.328636" y="0.0099999998">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="84.355804" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="96.958832" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="101.12233" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.03577" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="109.19926" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="115.45077" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.41541" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.57892" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="132.49236" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.43152" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="150.77174" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="159.94894" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="169.82631" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="181.60414" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="185.76764" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="189.68108" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6099997" y="20.48">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.174555" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.351757" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.629463" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.792961" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.807384" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="54.970882" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.884323" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="65.823486" y="20.48">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="77.176208" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="87.691238" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="91.854736" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.731384" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.67055" y="20.48">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="117.02327" y="20.48">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.05044" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="136.56546" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="140.72896" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="147.60561" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="151.7691" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="328.92001" y="9.8900003">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="333.0835" y="9.8900003">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="339.33499" y="9.8900003">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="345.58649" y="9.8900003">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span><br>用(<一个href="#EEq27">32</一个>)(<gydF4y2Ba一个href="#EEq29">34</一个>)的收益率<年代p一个nclass="equation" id="EEq30">
<svg height="155.375" id="M152" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 155.375" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,155.375)">
<g transform="translate(72,52.3)">
<text transform="matrix(1,0,0,-1,57.26,63.77)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-7.8800001" y="2.54">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,56.57,58.11)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,63.53,61.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.703768" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,96.78,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,105.57,61.24)">
<tspan style="font-size: 12.50px; " x="14.33" y="0.039999999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3400002" y="64.489998">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.99" y="64.480003">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="246.97" y="67">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.49" y="0.0099999998">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.054556" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.231758" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.509464" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.672962" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.988419" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.328636" y="0.0099999998">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="84.355804" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="96.958832" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="101.12233" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.03577" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="109.19926" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="115.45077" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.41541" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.57892" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="132.49236" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.43152" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="150.77174" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="159.94894" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="169.82631" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="181.60414" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="185.76764" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="189.68108" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="196.62024" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="207.96046" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="217.13766" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="225.83975" y="0.0099999998">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="234.86691" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="245.39444" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="249.55794" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="256.4346" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.8400002" y="20.48">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.180222" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.357424" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.059509" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.574535" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.738033" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.614681" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="66.566353" y="20.48">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="77.90657" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="87.083771" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.373985" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="102.53748" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="114.84043" y="20.48">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.18066" y="20.48">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="135.20782" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="147.82335" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="151.98685" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="155.90028" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="160.06378" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="166.30278" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="175.26743" y="20.48">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="179.43094" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="183.34438" y="20.48">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.8400002" y="40.950001">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.180222" y="40.950001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.357424" y="40.950001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.059509" y="40.950001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.574535" y="40.950001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.738033" y="40.950001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.614681" y="40.950001">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="66.566353" y="40.950001">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="77.90657" y="40.950001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="84.958267" y="40.950001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="92.547585" y="40.950001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="96.711082" y="40.950001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="100.62452" y="40.950001">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.15" y="64.489998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.68907" y="64.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.866272" y="64.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.931187" y="64.489998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="61.333923" y="64.489998">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.685448" y="64.489998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="74.224518" y="64.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="86" y="64.480003">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.163498" y="64.480003">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="94.076935" y="64.480003">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.239998" y="64.489998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="109.64274" y="64.489998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="120.98296" y="64.489998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="127.52203" y="64.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="136.69923" y="64.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="145.90144" y="64.489998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="157.30417" y="64.489998">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="163.6557" y="64.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="172.70787" y="64.489998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="184.0481" y="64.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="191.03999" y="64.480003">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="197.27899" y="64.480003">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="202.14267" y="64.480003">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="208.39417" y="64.480003">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="218.80916" y="64.480003">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="222.97266" y="64.480003">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="230.56198" y="64.480003">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="234.72548" y="64.480003">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="238.63892" y="64.480003">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="242.80241" y="64.480003">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-26.33" y="89.269997">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-12.214113" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-5.6750441" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="1.914277" y="89.269997">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.077776" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.9912148" y="89.269997">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.154714" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.544947" y="89.269997">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.908974" y="89.269997">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.072472" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.611542" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.788746" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="61.853661" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="73.256393" y="89.269997">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="79.607918" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="86.146988" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.912308" y="89.269997">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="102.07581" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.98925" y="89.269997">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="110.15275" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="121.55548" y="89.269997">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="132.9082" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.44728" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="148.62448" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="157.82669" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="169.21692" y="89.269997">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="175.58095" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="181.85745" y="89.269997">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="188.79662" y="89.269997">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="200.13684" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="207.18854" y="89.269997">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="213.7276" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="221.31693" y="89.269997">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="225.48042" y="89.269997">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="229.39386" y="89.269997">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="233.55736" y="89.269997">
为</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,347.76,-22.69)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,88.51,-48.5)">
<tspan style="font-size: 12.50px; " x="180.12" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.50372" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.042789" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.219992" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.097363" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.412094" y="0">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="56.77" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.309071" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.080002" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="79.2435" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="83.156937" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="87.32" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.722733" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="110.06296" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="116.60203" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="125.77923" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="134.98143" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="146.38417" y="0.0099999998">
⋅</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="152.7357" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="161.78787" y="0.0099999998">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="173.12808" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="186.36" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="192.89906" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="200.49001" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="204.6535" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="208.56694" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="212.73" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="221.34457" y="0.0099999998">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="379.35999" y="-55.220001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="383.5235" y="-55.220001">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="389.77499" y="-55.220001">
5</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="396.02649" y="-55.220001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>然后,我们有<年代p一个nclass="equation" id="EEq31">
<svg height="18.887501" id="M153" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.887501" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.8875)">
<g transform="translate(72,-56.89)">
<text transform="matrix(1,0,0,-1,134.14,63.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-7.8800001" y="2.54">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,133.45,57.57)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,140.41,60.7)">
<tspan style="font-size: 12.50px; " x="75.290001" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.703768" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.519823" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.860043" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.919998" y="0.0099999998">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.459068" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.049999" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.213501" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.126938" y="0">
)</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,224.32,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,231.97,60.69)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.404896" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.943966" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.529999" y="-0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.693501" y="-0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.606937" y="-0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.77" y="0">
为</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.384567" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="235.89999" y="-0.63">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="240.06349" y="-0.63">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="246.315" y="-0.63">
6</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="252.5665" y="-0.63">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>根据滑模理论,我们得出这样的结论:系统的轨迹(<一个href="#EEq1">1</一个>)收敛于滑动面<年代vg height="13.45" id="M154" style="vertical-align:-2.21957pt;width:49.5px;" version="1.1" viewbox="0 0 49.5 13.45" width="49.5" 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">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.5013199" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.578258" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.205088" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.245476" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在一个有限的时间和保持在它之后。因此,完成证明。</年代p一个n></p><h4 id="simulation">4所示。模拟</gydF4y2Bah4>
<p>在本节中,我们使用Genesio的混沌系统来验证该方法的有效性。Genesio的系统额外的输入如下:<年代p一个nclass="equation" id="EEq32">
<svg height="41.349998" id="M155" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,41.35)">
<g transform="translate(72,-38.92)">
<text transform="matrix(1,0,0,-1,91.85,63.2)">
<tspan style="font-size: 12.50px; " x="82.129997" y="20.48">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
̇</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.6640992" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.2755461" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.439045" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.352484" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.991817" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.032206" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.996857" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.649174" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.989395" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.279602" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.4431" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="85.970627" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.134125" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="97.01078" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="103.94994" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="115.29016" y="0">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="124.31733" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="134.84485" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.00835" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="145.88501" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="152.82417" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="164.16438" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="172.17882" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="176.34232" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="180.25575" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="184.41925" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="191.35841" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="202.69864" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="212.576" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="224.35384" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="228.51733" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="232.43077" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="238.68227" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.449997" y="20.469999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="94.613503" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.526939" y="20.469999">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="106.16627" y="20.469999">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="118.19416" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.58367" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="135.54832" y="20.469999">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="139.71182" y="20.469999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="143.62526" y="20.469999">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="149.87675" y="20.469999">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="376.01999" y="10.86">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="380.1835" y="10.86">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="386.435" y="10.86">
7</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="392.68649" y="10.86">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span>在哪里<年代p一个nclass="equation" id="eq6">
<svg height="138.35001" id="M156" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 138.35001" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,138.35)">
<g transform="translate(72,38.68)">
<text transform="matrix(1,0,0,-1,88.68,31.32)">
<tspan style="font-size: 12.50px; " x="24.48" y="-25.57">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.48" y="-14.07">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.48" y="-2.5599999">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.48" y="8.9499998">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.48" y="20.450001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.48" y="31.9">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="111.51" y="-25.57">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="111.51" y="-14.07">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="111.51" y="-2.5599999">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="111.51" y="8.9499998">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="111.51" y="20.450001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="111.51" y="31.9">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.61" y="-25.57">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.61" y="-14.07">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.61" y="-2.5599999">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.61" y="8.9499998">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.61" y="20.450001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="158.61" y="31.9">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="164.24001" y="-23.129999">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="164.24001" y="1.88">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="164.24001" y="26.889999">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.49001" y="-25.57">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.49001" y="-14.07">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.49001" y="-2.5599999">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.49001" y="8.9499998">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.49001" y="20.450001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.49001" y="31.9">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="218.75999" y="-25.57">
⎡</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="218.75999" y="-14.07">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="218.75999" y="-2.5599999">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="218.75999" y="8.9499998">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="218.75999" y="20.450001">
⎢</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="218.75999" y="31.9">
⎣</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="224.39" y="-23.129999">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="224.39" y="1.88">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="224.39" y="26.889999">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="230.64" y="-25.57">
⎤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="230.64" y="-14.07">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="230.64" y="-2.5599999">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="230.64" y="8.9499998">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="230.64" y="20.450001">
⎥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="230.64" y="31.9">
⎦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="238.35001" y="0.0099999998">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-5.8200002" y="65.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.57" y="65.489998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="140.59" y="63.080002">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="146.44" y="60.57">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.427982" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.389999" y="-23.129999">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.98436" y="-23.129999">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="96.279846" y="-23.129999">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.389999" y="1.88">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.98436" y="1.88">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="96.279846" y="1.88">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.1" y="26.889999">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.664555" y="26.889999">
6</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.89249" y="26.889999">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.457043" y="26.889999">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="65.708542" y="26.889999">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="68.834297" y="26.889999">
9</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.085793" y="26.889999">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="87.313728" y="26.889999">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="95.878281" y="26.889999">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="102.12978" y="26.889999">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.25553" y="26.889999">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="119.22" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="134.38614" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="146.56406" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="178.2" y="0">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="193.36613" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="206.71935" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-29.719999" y="60.57">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-17.867155" y="60.57">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.090000004" y="62.450001">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.137934" y="62.450001">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.365868" y="62.450001">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.930424" y="62.450001">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.181923" y="62.450001">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.307674" y="62.450001">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="56.389999" y="60.57">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.556137" y="60.57">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="80.583305" y="60.57">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="91.110832" y="60.57">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="95.27433" y="60.57">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="102.15098" y="60.57">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="109.77781" y="60.57">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="121.8182" y="60.57">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="126.68187" y="60.57">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="130.1577" y="60.57">
n</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,241.99,-32.38)">
<tspan style="font-size: 8.75px; " x="0" y="0">
3</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,248.95,-29.24)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.24" y="2.52">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="83.940002" y="-7.2399998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0834389" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.18" y="0.0099999998">
,</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.346138" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.111462" y="0.0099999998">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.27496" y="0.0099999998">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.1884" y="0.0099999998">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.827732" y="0.0099999998">
=</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,338.46,-17)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
</gydF4y2Batspan>
</text>
<g>
<path d="m 325.02,-26.12 30.54,0" 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,-1,325.02,-38)">
<tspan style="font-size: 12.50px; " x="31.73" y="-8.75">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.278666" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.618887" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="142.85001" y="-51.540001">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="147.0135" y="-51.540001">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="153.265" y="-51.540001">
8</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="159.51649" y="-51.540001">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span></p>
<p>不失一般性,我们考虑<年代vg height="13.45" id="M157" style="vertical-align:-2.21957pt;width:38.612499px;" version="1.1" viewbox="0 0 38.612499 13.45" width="38.612499" 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">
Δ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.554453" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.63139" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是norm-bounded添加剂形式,在哪里<年代vg height="14.6" id="M158" style="vertical-align:-3.13504pt;width:83.525002px;" version="1.1" viewbox="0 0 83.525002 14.6" width="83.525002" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-52.69,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.191385" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.618887" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.033886" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.285385" y="0">
]</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="14.6" id="M159" style="vertical-align:-3.13504pt;width:67.012497px;" version="1.1" viewbox="0 0 67.012497 14.6" width="67.012497" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.02,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.68,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.604944" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.856443" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.982195" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.7125" id="M160" style="vertical-align:-3.13504pt;width:101.05px;" version="1.1" viewbox="0 0 101.05 14.7125" width="101.05" 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,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.22,60.28)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.35,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.703768" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.995659" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.121407" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.460907" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.324574" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="53.800407" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="64.215408" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="14.6" id="M161" style="vertical-align:-3.13504pt;width:31.174999px;" version="1.1" viewbox="0 0 31.174999 14.6" width="31.174999" 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">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.22,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.35,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>满足<年代vg height="19.362499" id="M162" style="vertical-align:-4.22832pt;width:175.16251px;" version="1.1" viewbox="0 0 175.16251 19.362499" width="175.16251" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.3625)">
<g transform="translate(72,-56.51)">
<text transform="matrix(1,0,0,-1,-71.95,60.78)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.41,65.78)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.8099999" y="9.2200003">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.7,60.78)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.240437" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-35.73,57.65)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.86,60.78)">
<tspan style="font-size: 12.50px; " x="0" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.0769377" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.716271" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.744158" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.995659" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.121407" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.372906" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.624409" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="54.488075" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="57.963909" y="0">
n</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,35.45,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,42.41,60.78)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.37677" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.417158" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。此外,我们选择<年代vg height="13.125" id="M163" style="vertical-align:-1.95624pt;width:75.25px;" version="1.1" viewbox="0 0 75.25 13.125" width="75.25" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.125)">
<g transform="translate(72,-61.5)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.640533" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.680922" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.844421" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.259418" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.68692" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.938423" y="0">
]</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="13.7375" id="M164" style="vertical-align:-2.34499pt;width:70.4375px;" version="1.1" viewbox="0 0 70.4375 13.7375" width="70.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.7375)">
<g transform="translate(72,-61.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.8148546" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.855244" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.106745" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.232494" y="0">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.483994" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.735493" y="0">
6</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.986996" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba然后,求解lmi (<一个href="#EEq20">25</一个>)和(<一个href="#EEq21">26</一个>)的收益率<年代p一个nclass="equation" id="eq7">
<svg height="31.387501" id="M165" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,31.3875)">
<g transform="translate(72,-46.89)">
<text transform="matrix(1,0,0,-1,121.4,56.32)">
<tspan style="font-size: 12.50px; " x="25.030001" y="4.9200001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="163.00999" y="4.9200001">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.990617" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.77" y="1.87">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.0215" y="1.87">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.147251" y="1.87">
6</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.39875" y="1.87">
5</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.650249" y="1.87">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.901749" y="1.87">
5</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="71.129684" y="1.87">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="79.694237" y="1.87">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="85.94574" y="1.87">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="89.071487" y="1.87">
8</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="95.32299" y="1.87">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="101.57449" y="1.87">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="107.82599" y="1.87">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="120.05392" y="1.87">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="128.61848" y="1.87">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="134.86998" y="1.87">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="137.99573" y="1.87">
8</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="144.24722" y="1.87">
9</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="150.49873" y="1.87">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="156.75023" y="1.87">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="170.83" y="0">
。</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="346.47" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="350.63348" y="0">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="356.88501" y="0">
9</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="363.13651" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg></span></p>
<p>初始值是<年代vg height="16.2875" id="M166" style="vertical-align:-2.21957pt;width:116.65px;" version="1.1" viewbox="0 0 116.65 16.2875" width="116.65" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2875)">
<g transform="translate(72,-58.97)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.8766499" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.291649" y="0">
)</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.91848" y="0">
=</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.958866" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.122368" y="0">
3</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.537365" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="64.740532" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="76.080757" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="82.332253" y="0">
]</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,14.55,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。仿真结果如图<一个href="//www.newsama.com/journals/jcse/2011/859159/fig2/" target="_blank">2</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jcse/2011/859159/fig3/" target="_blank">3</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jcse/2011/859159/fig4/" target="_blank">4</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jcse/2011/859159/fig5/" target="_blank">5</一个>。</p><d我v 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="859159.fig.002" src="https://static-01.hindawi.com/articles/jcse/volume-2011/859159/figures/859159.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p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/859159/fig2/" title="" target="_blank"></a>
</div>
<div class="floats-partial-caption-text">
<table>
不受控制的Genesio阶段曲线的系统。</gydF4y2Batable>
</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="859159.fig.003" src="https://static-01.hindawi.com/articles/jcse/volume-2011/859159/figures/859159.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p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/859159/fig3/" title="" target="_blank"></a>
</div>
<div class="floats-partial-caption-text">
<svg height="13.45" id="M167" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 24.025 13.45" width="24.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.8766499" y="0">
(</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.953588" y="0">
)</gydF4y2Batspan>
</text>
</g>
</g>
</svg>
<table>
状态Gene年代我o控制的系统。</gydF4y2Batable>
</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="859159.fig.004" src="https://static-01.hindawi.com/articles/jcse/volume-2011/859159/figures/859159.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p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/859159/fig4/" title="" target="_blank"></a>
</div>
<div class="floats-partial-caption-text">
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<span class="caption-text">图5</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jcse/2011/859159/fig5/" title="" target="_blank"></a>
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滑模gydF4y2Ba。</gydF4y2Batable>
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<p>图<一个href="//www.newsama.com/journals/jcse/2011/859159/fig2/" target="_blank">2</一个>显示了不受控制的相位曲线Genesio的系统。图<一个href="//www.newsama.com/journals/jcse/2011/859159/fig3/" target="_blank">3</一个>显示的时间响应状态<年代vg height="13.45" id="M170" style="vertical-align:-2.21957pt;width:24.025px;" version="1.1" viewbox="0 0 24.025 13.45" width="24.025" xmlns="http://www.w3.org/2000/svg">
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</svg>Genesio控制的系统。图<一个href="//www.newsama.com/journals/jcse/2011/859159/fig4/" target="_blank">4</一个>显示了控制输入响应曲线。滑模响应曲线如图<一个href="//www.newsama.com/journals/jcse/2011/859159/fig5/" target="_blank">5</一个>。从仿真结果,结果表明,该方法是有效的。</p><gydF4y2Bah4 id="conclusion">5。结论</gydF4y2Bah4>
<p>本文非脆弱的问题与外部扰动不确定混沌系统的滑模控制研究。提出了一种新的滑动面,充分条件导出广义的渐近稳定<年代vg height="14.2375" id="M171" style="vertical-align:-3.13504pt;width:19.862499px;" version="1.1" viewbox="0 0 19.862499 14.2375" width="19.862499" xmlns="http://www.w3.org/2000/svg">
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</svg>干扰抑制水平滑模动态。建立非脆弱滑模控制器使系统状态到达滑动面在一个有限的时间。最后,仿真显示了该方法的有效性。</p><gydF4y2Bah4 id="acknowledgment">承认</gydF4y2Bah4>
<p>作者感谢中国国家自然科学基金的支持下拨款61074003和61074003号。</p></d我v>
<div class="xml-content">
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</ol>
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<h4 class="copyright" id="copyright">版权</gydF4y2Bah4>
<p>版权©2011 Leipo刘et al。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。</p></d我v>
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<div class="sc-hBbWxd kdRRST">
<div class="sc-dyGzUR cHatnS">
<div>
的观点<年代p一个n>858年年</年代p一个n></d我v>
<div>
下载<年代p一个n>765年年</年代p一个n></d我v>
</div>
<div>
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<span class="__dimensions_badge_embed__" data-doi="10.1155/2011/859159" data-style="small_circle"></span>引用</d我v>
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