Document Zbl 1283.93147

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A concept of general Lyapunov-like functions is presented. A necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized Lyapunov-like functions, which enables derivation of improved stability tests, an $L_{2}$-gain characterization and a design method for stabilizing switching laws. A solution to the $H_\infty$ control problem for switched systems is also provided.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6271358">Cited in <strong>322</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A93B36" title="MSC2020">93B36</a> </td> <td class="space"> $H^\infty$-control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D05" title="MSC2020">93D05</a> </td> <td class="space"> Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.) in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aswitched+systems">switched systems</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Amultiple+Lyapunov+functions">multiple Lyapunov functions</a>; <a href="/?q=ut%3A%5C%28L_2%5C%29-gain">$L_2$-gain</a>; <a href="/?q=ut%3A%5C%28H_%5Cinfty%5C%29+control">$H_\infty$ control</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 1283.93147" data-ciurl="/ci/06271358" data-biburl="/bibtex/06271358.bib" data-amsurl="/amsrefs/06271358.bib" data-xmlurl="/xml/06271358.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06271358.pdf" title="Zbl 1283.93147 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.automatica.2007.10.011" aria-label="DOI for “On stability, $L_2$-gain and $H_\infty$ control for switched systems”" title="10.1016/j.automatica.2007.10.011">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://hdl.handle.net/1885/36098" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bacciotti, A., Stabilization by means of state space depending switching rules, Systems & Control Letters, 53, 3, 195-201 (2004) · <a href="/1157.93480" class="nowrap">Zbl 1157.93480</a></td> </tr><tr> <td>[2]</td> <td class="space">Banerjee, A.; Arkun, Y.; Pearson, R.; Ogunnaike, B., $H_\infty$ control of nonlinear processes using multiple linear models, (Murray-Smith, R.; Johansen, T. 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