Document Zbl 1218.34082

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Math. Comput.</a> <a href="/?q=in%3A275207" title="Articles in this Issue">217, No. 12, 5982-5993 (2011)</a>. </div> <div class="abstract">Consider the class of linear switched delay systems with time-varying exogenous disturbances <br class="zbmathjax-paragraph">\[ \begin{aligned}\dot x(t)&=A_{\sigma(t)}x(t)+B_{\sigma(t)}x(t-h)+G_{\sigma(t)}\omega(t),\\ z(t)&= C_{\sigma(t)}x(t)+D_{\sigma(t)}\omega(t),\quad t\geq 0,\tag{1}\\ x(t)&=\varphi(t),\quad t\in[-h,0], \end{aligned} \]<br class="zbmathjax-paragraph">where $x(t)\in\mathbb R^n$ is the state, $z(t)\in\mathbb R^m$ is the output, $\omega(t)$ is a time-varying exogenous disturbance meeting the constraint $\int_0^{\infty}\omega^{\top}(t)\omega(t)\,dt\leq d$, $\sigma(t):[0,\infty)\to M=\{1,2,\dots,m\}$ is the switching signal. Sufficient conditions are given which guarantee that (1) is finite-time bounded and has finite-time weighted $L_2$-gain. These conditions are delay-dependent and are given in terms of linear matrix inequalities and a condition of the form $\tau_a>\tau_a^*$ where $\tau_a$ is an average dwell-time. The proofs are based on Lyapunov functionals. A numerical example is given to verify the efficiency of the proposed method.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A12452">Nataliya O. Sedova (Ulyanovsk)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5862539">Cited in <strong>79</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K12" title="MSC2020">34K12</a> </td> <td class="space"> Growth, boundedness, comparison of solutions to functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K35" title="MSC2020">34K35</a> </td> <td class="space"> Control problems for functional-differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aswitched+linear+systems">switched linear systems</a>; <a href="/?q=ut%3Atime-delay">time-delay</a>; <a href="/?q=ut%3Afinite-time+boundedness">finite-time boundedness</a>; <a href="/?q=ut%3ALyapunov+functional">Lyapunov functional</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1218.34082" data-ciurl="/ci/05862539" data-biburl="/bibtex/05862539.bib" data-amsurl="/amsrefs/05862539.bib" data-xmlurl="/xml/05862539.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05862539.pdf" title="Zbl 1218.34082 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.amc.2010.12.032" aria-label="DOI for “Finite-time boundedness and $L_{2}$-gain analysis for switched delay systems with norm-bounded disturbance”" title="10.1016/j.amc.2010.12.032">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Liberzon, D.; Morse, A. 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