Document Zbl 1390.93195

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J. Robust Nonlinear Control</a> <a href="/?q=in%3A373237" title="Articles in this Issue">28, No. 2, 381-402 (2018)</a>. </div> <div class="abstract">Summary: This paper focuses on the problem of finite-time $H_\infty$ control for one family of discrete-time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete-time close-loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite-time boundedness and sliding mode $H_\infty$ finite-time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6866136">Cited in <strong>28</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr><tr> <td class="mono"> 60J75 </td> <td class="space"> Jump processes (MSC2010) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E03" title="MSC2020">93E03</a> </td> <td class="space"> Stochastic systems in control theory (general) </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3A%5C%28H_%5Cinfty%5C%29+finite-time+boundedness">$H_\infty$ finite-time boundedness</a>; <a href="/?q=ut%3Alinear+matrix+inequalities+%28LMIs%29">linear matrix inequalities (LMIs)</a>; <a href="/?q=ut%3Arandomly+occurring+nonlinearities+%28RONs%29">randomly occurring nonlinearities (RONs)</a>; <a href="/?q=ut%3Asensor+fault">sensor fault</a>; <a href="/?q=ut%3Asingular+Markovian+jump+systems">singular Markovian jump systems</a>; <a href="/?q=ut%3Asliding+mode+control">sliding mode control</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 1390.93195" data-ciurl="/ci/06866136" data-biburl="/bibtex/06866136.bib" data-amsurl="/amsrefs/06866136.bib" data-xmlurl="/xml/06866136.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06866136.pdf" title="Zbl 1390.93195 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/10.1002/rnc.3872" aria-label="DOI for “Reliable sliding mode finite-time control for discrete-time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities”" title="10.1002/rnc.3872">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">Blanke, M.; 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Document Zbl 1390.93195 - zbMATH Open