Document Zbl 1373.93268

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The stabilization is achieved by only exerting impulsive action on the slow state variables. Two novel Lyapunov methods are presented to determine exponential stability of the impulsively controlled systems. For the case where the time-delay is unknown and may be time-varying, a Lyapunov-Razumikhin method is developed, in which the Razumikhin condition is constructed by exploiting the relation among the fast state variables, the slow state variables, and their initial values. For the case where the delay derivative is strictly less than 1, a descriptor type of impulse-time-dependent Lyapunov functional is introduced, which is discontinuous at impulse times but does not grow along the state trajectories by construction. By using a convex technique, the stability criteria are expressed in terms of Linear Matrix Inequalities (LMIs). Then, the impulsive controllers can be designed in the framework of LMIs. The effectiveness and advantages of the proposed methods are confirmed through simulation results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6803917">Cited in <strong>38</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D09" title="MSC2020">93D09</a> </td> <td class="space"> Robust stability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D21" title="MSC2020">93D21</a> </td> <td class="space"> Adaptive or robust stabilization </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><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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aimpulsive+stabilization">impulsive stabilization</a>; <a href="/?q=ut%3Asingular+systems">singular systems</a>; <a href="/?q=ut%3Atime-varying+delay">time-varying delay</a>; <a href="/?q=ut%3Aimpulse-time-dependent+Lyapunov+function%2Ffunctional">impulse-time-dependent Lyapunov function/functional</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 1373.93268" data-ciurl="/ci/06803917" data-biburl="/bibtex/06803917.bib" data-amsurl="/amsrefs/06803917.bib" data-xmlurl="/xml/06803917.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06803917.pdf" title="Zbl 1373.93268 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.2017.05.008" aria-label="DOI for “Impulsive stabilization of a class of singular systems with time-delays”" title="10.1016/j.automatica.2017.05.008">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">Briat, C.; Seuret, A., Convex dwell-time characterizations for uncertain linear impulsive systems, IEEE Transactions on Automatic Control, 57, 12, 3241-3246 (2012) · <a href="/1369.34075" class="nowrap">Zbl 1369.34075</a></td> </tr><tr> <td>[2]</td> <td class="space">Briat, C.; Seuret, A., A looped-functional approach for robust stability analysis of linear impulsive systems, Systems & Control Letters, 61, 10, 980-988 (2012) · <a href="/1270.93084" class="nowrap">Zbl 1270.93084</a></td> </tr><tr> <td>[3]</td> <td class="space">Chadli, M.; Darouach, M., Further enhancement on robust control design for discrete-time singular systems, IEEE Transactions on Automatic Control, 59, 2, 494-499 (2014) · <a href="/1360.93382" class="nowrap">Zbl 1360.93382</a></td> </tr><tr> <td>[4]</td> <td class="space">Chen, W.-H.; Li, D. 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