Document Zbl 1416.93158

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K.</a>; <a href="/authors/wu.ligang" title="Author Profile">Wu, Ligang</a></div> <h2 class="title"> <strong>Necessary and sufficient stability condition for second-order switched systems: a phase function approach.</strong> <i>(English)</i> <a class="label nowrap" href="/1416.93158">Zbl 1416.93158</a> </h2> <div class="source"> <a href="/serials/95" title="Journal Profile">Int. J. Control</a> <a href="/?q=in%3A434107" title="Articles in this Issue">92, No. 4, 926-939 (2019)</a>. </div> <div class="abstract">Summary: To find a unified approach for the stability analysis of second-order switched system, the concept of phase function is proposed in this paper. First, the basic properties of phase function are explored. Following this concept and its properties, the phase-based stability criterion is investigated based on the Lyapunov theory, and a necessary and sufficient stability condition is obtained in the phase function approach. Moreover, the connection between phase-based stability conditions and algebraic condition of system matrices is also discussed. Finally, numerical examples are provided to exemplify the main result and make necessary comparisons with the existing methods.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7067353">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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><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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aphase+function">phase function</a>; <a href="/?q=ut%3Aswitched+system">switched system</a>; <a href="/?q=ut%3Astability+analysis">stability analysis</a>; <a href="/?q=ut%3ALyapunov+function">Lyapunov function</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 1416.93158" data-ciurl="/ci/07067353" data-biburl="/bibtex/07067353.bib" data-amsurl="/amsrefs/07067353.bib" data-xmlurl="/xml/07067353.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07067353.pdf" title="Zbl 1416.93158 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/10.1080/00207179.2017.1375157" aria-label="DOI for “Necessary and sufficient stability condition for second-order switched systems: a phase function approach”" title="10.1080/00207179.2017.1375157">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://kclpure.kcl.ac.uk/portal/en/publications/necessary-and-sufficient-stability-condition-for-secondorder-switched-systems(4d53aaa6-ee64-4da5-865f-e7e46a994369).html" 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">Blanchini, F., Set invariance in control, <span class="zbmathjax-textit">Automatica</span>,, 35, 11, 1747-1767 (1999) · <a href="/0935.93005" class="nowrap">Zbl 0935.93005</a></td> </tr><tr> <td>[2]</td> <td class="space">Chesi, G.; Garulli, A.; Tesi, A.; Vicino, A., Homogeneous Lyapunov functions for systems with structured uncertainties, <span class="zbmathjax-textit">Automatica</span>,, 39, 6, 1027-1035 (2003) · <a href="/1079.93036" class="nowrap">Zbl 1079.93036</a></td> </tr><tr> <td>[3]</td> <td class="space">Chesi, G.; Colaneri, P.; Geromel, J. 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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