Document Zbl 1293.93683

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Franklin Inst.</a> <a href="/?q=in%3A335412" title="Articles in this Issue">350, No. 5, 1075-1092 (2013)</a>. </div> <div class="abstract">Summary: This paper considers the finite time stability and finite time boundedness problems for switched linear systems subject to $L_2$ disturbances. Differently from the existing average dwell-time technique, state-dependent switching control strategy is used to design the switching rule, which does not require the switching instants to be known in advance. Sufficient conditions for the switched systems to be finite time stable and finite time bounded are derived; the occurrence of sliding motion will not destroy the stability with the proposed conditions. Moreover, $L_2$-gain analysis problem is also considered. The proposed conditions are given in terms of linear matrix inequalities. Several examples are given to illustrate the effectiveness of the proposed methods.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6329023">Cited in <strong>20</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D99" title="MSC2020">93D99</a> </td> <td class="space"> Stability of control systems </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%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%3Afinite+time+stability">finite time stability</a>; <a href="/?q=ut%3Afinite+time+boundedness">finite time boundedness</a>; <a href="/?q=ut%3Aswitched+linear+systems">switched linear systems</a>; <a href="/?q=ut%3A%5C%28L_2%5C%29+disturbances">$L_2$ disturbances</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 1293.93683" data-ciurl="/ci/06329023" data-biburl="/bibtex/06329023.bib" data-amsurl="/amsrefs/06329023.bib" data-xmlurl="/xml/06329023.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06329023.pdf" title="Zbl 1293.93683 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.2013.02.004" aria-label="DOI for “Finite time stability and $L_2$-gain analysis for switched linear systems with state-dependent switching”" title="10.1016/j.jfranklin.2013.02.004">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">Skafidas, E.; Evans, R. 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