Document Zbl 1162.93030

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Based on the backstepping method and the control Lyapunov function approach, it is shown that, under a simultaneous domination assumption, a switched nonlinear system in strict-feedback form can be globally uniformly asymptotically stabilized by a continuous state feedback controller. A universal formula for constructing stabilizing feedback laws is presented. One example is included for verifying the obtained results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5564302">Cited in <strong>124</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A93C15" title="MSC2020">93C15</a> </td> <td class="space"> Control/observation systems governed by ordinary differential equations </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%3A93D20" title="MSC2020">93D20</a> </td> <td class="space"> Asymptotic stability in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Abackstepping">backstepping</a>; <a href="/?q=ut%3Acontrol+Lyapunov+function">control Lyapunov function</a>; <a href="/?q=ut%3Anonlinear+control+systems">nonlinear control systems</a>; <a href="/?q=ut%3Astrict-feedback+form">strict-feedback form</a>; <a href="/?q=ut%3Aswitched+systems">switched 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 1162.93030" data-ciurl="/ci/05564302" data-biburl="/bibtex/05564302.bib" data-amsurl="/amsrefs/05564302.bib" data-xmlurl="/xml/05564302.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05564302.pdf" title="Zbl 1162.93030 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.2008.12.004" aria-label="DOI for “Stabilizing controllers design for switched nonlinear systems in strict-feedback form”" title="10.1016/j.automatica.2008.12.004">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">Artstein, Z., Stabilization with relaxed control, Nonlinear Analysis, Theory, Methods & Applications, 7, 1163-1173 (1983) · <a href="/0525.93053" class="nowrap">Zbl 0525.93053</a></td> </tr><tr> <td>[2]</td> <td class="space">Branicky, M. 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