Document Zbl 1544.93614

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Unlike the hybrid conditions derived in previous literature, this study used a novel time-dependent quadratic Lyapunov function approach and a convex sufficient condition for switched linear systems is proposed in the framework of bounded maximum average dwell time (BMADT). The resulting condition in this study is enforced using the sum of squares programming. Then, the condition for switched linear systems is extended to uncertain systems and the robust stability condition is derived. Moreover, a new stability result of continuous-time switched systems with all subsystems unstable is investigated based on the BMADT conditions. The simulation shows that it is better than the results in previous literature. Two numerical examples are proposed to illustrate the authors’ approach.<br class="zbmathjax-paragraph">© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7907009">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D09" title="MSC2020">93D09</a> </td> <td class="space"> Robust stability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D20" title="MSC2020">93D20</a> </td> <td class="space"> Asymptotic stability in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C30" title="MSC2020">93C30</a> </td> <td class="space"> Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D30" title="MSC2020">93D30</a> </td> <td class="space"> Lyapunov and storage functions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C05" title="MSC2020">93C05</a> </td> <td class="space"> Linear systems in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Arobust+control">robust control</a>; <a href="/?q=ut%3Atime-varying+systems">time-varying systems</a>; <a href="/?q=ut%3Alinear+systems">linear systems</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Aasymptotic+stability">asymptotic stability</a>; <a href="/?q=ut%3ALyapunov+methods">Lyapunov methods</a>; <a href="/?q=ut%3Adiscrete+time+systems">discrete time systems</a>; <a href="/?q=ut%3Auncertain+systems">uncertain systems</a>; <a href="/?q=ut%3Acontinuous+time+systems">continuous time systems</a>; <a href="/?q=ut%3Astability+problem">stability problem</a>; <a href="/?q=ut%3Acontinuous-time+switched+systems">continuous-time switched systems</a>; <a href="/?q=ut%3Aunstable+subsystems">unstable subsystems</a>; <a href="/?q=ut%3Ahybrid+conditions">hybrid conditions</a>; <a href="/?q=ut%3Aprevious+Literature">previous Literature</a>; <a href="/?q=ut%3Anovel+time-dependent+quadratic+Lyapunov+function+approach">novel time-dependent quadratic Lyapunov function approach</a>; <a href="/?q=ut%3Aconvex+sufficient+condition">convex sufficient condition</a>; <a href="/?q=ut%3Aswitched+linear+systems">switched linear systems</a>; <a href="/?q=ut%3Aresulting+condition">resulting condition</a>; <a href="/?q=ut%3Auncertain+systems">uncertain systems</a>; <a href="/?q=ut%3Arobust+stability+condition">robust stability condition</a>; <a href="/?q=ut%3Astability+result">stability result</a>; <a href="/?q=ut%3ABMADT+conditions">BMADT conditions</a></div> <div class="software"> <h3>Software:</h3><a href="/software/891">Sostools</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 1544.93614" data-ciurl="/ci/07907009" data-biburl="/bibtex/07907009.bib" data-amsurl="/amsrefs/07907009.bib" data-xmlurl="/xml/07907009.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07907009.pdf" title="Zbl 1544.93614 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/10.1049/iet-cta.2019.0018" aria-label="DOI for “New result on robust stability of switched systems with all subsystems unstable”" title="10.1049/iet-cta.2019.0018">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">Goebel, R.; Sanfelice, R. 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