Document Zbl 1454.93238

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Franklin Inst.</a> <a href="/?q=in%3A456468" title="Articles in this Issue">357, No. 18, 13552-13568 (2020)</a>. </div> <div class="abstract">Summary: The switched system with possible unstable modes is investigated by employing both stabilizing and destabilizing switching instants under the time-dependent switching signal. A new piece-wise Lyapunov function is proposed to distinguish the property of the switching instants with the help of dwell time information. Then, globally exponentially stable conditions of the switched nonlinear system and the switched linear system are derived, respectively, which compensate the state divergence resulted from unstable modes and destabilizing switching instants by stabilizing switching instants. The related result is extended to the controller design of the switched linear system. Besides, for the switched linear systems with pairwise commutative, a necessary and sufficient condition is proposed based on a new time-dependent switching signal, which provides a novel way for the controller design of the switched system. Finally, simulation is presented to show the effectiveness of our results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7289803">Cited in <strong>9</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D23" title="MSC2020">93D23</a> </td> <td class="space"> Exponential stability </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%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </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%3Aswitched+nonlinear+systems">switched nonlinear systems</a>; <a href="/?q=ut%3Aexponential+stabilization">exponential stabilization</a>; <a href="/?q=ut%3Aswitched+linear+systems">switched linear systems</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 1454.93238" data-ciurl="/ci/07289803" data-biburl="/bibtex/07289803.bib" data-amsurl="/amsrefs/07289803.bib" data-xmlurl="/xml/07289803.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07289803.pdf" title="Zbl 1454.93238 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.jfranklin.2020.10.007" aria-label="DOI for “Stabilization of switched systems with time-dependent switching signal”" title="10.1016/j.jfranklin.2020.10.007">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">Brockett, R. 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