Document Zbl 1074.93025

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S.</a></div> <h2 class="title"> <strong>Analysis and synthesis of switched linear control systems.</strong> <i>(English)</i> <a class="label nowrap" href="/1074.93025">Zbl 1074.93025</a> </h2> <div class="source"> <a href="/serials/348" title="Journal Profile">Automatica</a> <a href="/?q=in%3A113009" title="Articles in this Issue">41, No. 2, 181-195 (2005)</a>. </div> <div class="abstract">Recently, switched control systems have been attracting much attention because the problems are not only academically challenging, but also of practical importance. The paper provides a concise and timely survey on analysis and synthesis of switched linear control systems described by \[ \begin{aligned} \delta x(t)&=A_{\sigma}x(t)+B_{\sigma}u(t),\\ y(t)&=C_{\sigma}x(t), \end{aligned} \] where $x\in\mathbb R^n$ is the state, $u\in\mathbb R^p$ is the control input, $\sigma$ is the piecewise constant switching signal taking values from the finite index set $\mathcal F=\{1,2,\dots ,m\}$, $\delta$ denotes the derivative operator in continuous time ($\delta x(t)=(d/dt)x(t)$) and the shift-forward operator in discrete time ($\delta x(t)=x(t+1)$). The paper presents the basic concepts and main properties of switched linear control systems in a systematic manner. The fundamental topics include<br class="zbmathjax-paragraph">(i) controllability and observability,<br class="zbmathjax-paragraph">(ii) system structural decomposition,<br class="zbmathjax-paragraph">(iii) feedback controller design for stabilization, and<br class="zbmathjax-paragraph">(iv) optimal control.<br class="zbmathjax-paragraph">The paper includes a useful and rich list of references.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A2863">Georgy Osipenko (St. Peterburg)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A2137840">Cited in <strong>218</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%3A93-02" title="MSC2020">93-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to systems and control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B05" title="MSC2020">93B05</a> </td> <td class="space"> Controllability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D15" title="MSC2020">93D15</a> </td> <td class="space"> Stabilization of systems by feedback </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B12" title="MSC2020">93B12</a> </td> <td class="space"> Variable structure systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C65" title="MSC2020">93C65</a> </td> <td class="space"> Discrete event control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aswitched+linear+control+systems">switched linear control systems</a>; <a href="/?q=ut%3Aswitching+signal">switching signal</a>; <a href="/?q=ut%3Astabilization">stabilization</a>; <a href="/?q=ut%3Acontrollability">controllability</a>; <a href="/?q=ut%3Aobservability">observability</a>; <a href="/?q=ut%3Aoptimal+control">optimal control</a>; <a href="/?q=ut%3Ahybrid+systems">hybrid systems</a>; <a href="/?q=ut%3Astructural+decomposition">structural decomposition</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 1074.93025" data-ciurl="/ci/02137840" data-biburl="/bibtex/02137840.bib" data-amsurl="/amsrefs/02137840.bib" data-xmlurl="/xml/02137840.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02137840.pdf" title="Zbl 1074.93025 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.2004.09.015" aria-label="DOI for “Analysis and synthesis of switched linear control systems”" title="10.1016/j.automatica.2004.09.015">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">Aubin, J. 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