Document Zbl 1497.93234

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Math. Comput.</a> <a href="/?q=in%3A460195" title="Articles in this Issue">386, Article ID 125443, 19 p. (2020)</a>. </div> <div class="abstract">Summary: The paper investigates the issue of mixed $H_\infty$ and dissipative asynchronous controller design for a class of Markov jump singularly perturbed systems (MJSPSs). A suitable dynamic event-triggered rule is offered to further mitigate the transmission burden of communication network. Since the mode information of Markov chain is extremely difficult to get, an asynchronous controller is well constructed. Hence, a hidden Markov model (HMM) is chosen to describe the non-synchronous facts between states of the original Markov chain and the constructed non-synchronous controller. Resorting to the Lyapunov functional concerning the internal dynamic variable, sufficient conditions of stochastically stable with a certain mixed $H_\infty$ and dissipative performance for the resulting closed-loop MJSPSs are offered. Based on the LMI technique, the design framework of asynchronous controller and the dynamic event-triggered rule are given in a unified way. Lastly, a modified DC motor model is offered to demonstrate the superiority of the proffered method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7323475">Cited in <strong>36</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E15" title="MSC2020">93E15</a> </td> <td class="space"> Stochastic stability in control theory </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%3A93C70" title="MSC2020">93C70</a> </td> <td class="space"> Time-scale analysis and singular perturbations in control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60J28" title="MSC2020">60J28</a> </td> <td class="space"> Applications of continuous-time Markov processes on discrete state spaces </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AMarkov+jump+singularly+perturbed+systems">Markov jump singularly perturbed systems</a>; <a href="/?q=ut%3Adynamic+event-triggered+rule">dynamic event-triggered rule</a>; <a href="/?q=ut%3Aasynchronous+control">asynchronous control</a>; <a href="/?q=ut%3Ahidden+Markov+model">hidden Markov model</a>; <a href="/?q=ut%3Alinear+matrix+inequality">linear matrix inequality</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 1497.93234" data-ciurl="/ci/07323475" data-biburl="/bibtex/07323475.bib" data-amsurl="/amsrefs/07323475.bib" data-xmlurl="/xml/07323475.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07323475.pdf" title="Zbl 1497.93234 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.amc.2020.125443" aria-label="DOI for “Dynamic event-based mixed $H_\infty$ and dissipative asynchronous control for Markov jump singularly perturbed systems”" title="10.1016/j.amc.2020.125443">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">Kokotovic, P. 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