Document Zbl 1443.93014

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Math. Modelling</a> <a href="/?q=in%3A443800" title="Articles in this Issue">40, No. 1, 302-314 (2016)</a>. </div> <div class="abstract">Summary: This paper investigates the problem of finite-time $H_\infty$ control for a class of singular Markovian jump systems with partly unknown transition rates. Firstly, sufficient conditions on singular stochastic finite-time boundedness of singular Markovian jump systems with partly unknown transition rates are obtained. Secondly, the results are extended to singular stochastic $H_\infty$ finite-time boundedness of singular Markovian jump systems with partly unknown transition rates. Then state feedback controllers are designed to ensure the singular stochastic finite-time boundedness and the singular stochastic $H_\infty$ finite-time boundedness of the underlying closed singular Markovian jump systems in the forms of strict LMIs. Finally, numerical examples are given to illustrate the validity of the proposed methods.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7149567">Cited in <strong>19</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93-10" title="MSC2020">93-10</a> </td> <td class="space"> Mathematical modeling or simulation for problems pertaining to systems and control theory </td> </tr><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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asingular+Markovian+jump+systems">singular Markovian jump systems</a>; <a href="/?q=ut%3Asingular+stochastic+finite-time+stability">singular stochastic finite-time stability</a>; <a href="/?q=ut%3Asingular+stochastic+finite-time+boundedness">singular stochastic finite-time boundedness</a>; <a href="/?q=ut%3Apartly+unknown+transition+rates">partly unknown transition rates</a>; <a href="/?q=ut%3Alinear+matrix+inequalities+%28LMIs%29">linear matrix inequalities (LMIs)</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 1443.93014" data-ciurl="/ci/07149567" data-biburl="/bibtex/07149567.bib" data-amsurl="/amsrefs/07149567.bib" data-xmlurl="/xml/07149567.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07149567.pdf" title="Zbl 1443.93014 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.apm.2015.04.044" aria-label="DOI for “Finite-time $H_\infty$ control for singular Markovian jump systems with partly unknown transition rates”" title="10.1016/j.apm.2015.04.044">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">Dai, L., Singular Control Systems (1989), Springer: Springer Berlin · <a href="/0669.93034" class="nowrap">Zbl 0669.93034</a></td> </tr><tr> <td>[2]</td> <td class="space">Lewis, F., A survey of linear singular systems, Circ. 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