Document Zbl 07470949

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J. Syst. Sci., Princ. Appl. Syst. Integr.</a> <a href="/?q=in%3A476368" title="Articles in this Issue">50, No. 10, 2042-2052 (2019)</a>. </div> <div class="abstract">Summary: This paper studies the control synthesis for uncertain semi-Markov jump systems in a discrete-time domain subjected to external disturbance. The switching between modes is determined by a function of the transition probability and the sojourn-time distribution between two neighbouring modes. Based on the $\sigma $-error mean square stability criterion, time-varying controllers are designed to stabilise the system. By constructing a holding time dependent Lyapunov function, time-varying state-feedback controllers are obtained that meet a set of sufficient conditions in the form of linear matrix inequalities. Two examples, including a DC motor system, are presented to show the validity of the proposed control scheme.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7470949">Cited in <strong>6</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%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%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B52" title="MSC2020">93B52</a> </td> <td class="space"> Feedback control </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asemi-Markov+jump+system">semi-Markov jump system</a>; <a href="/?q=ut%3Aparameter+uncertainty">parameter uncertainty</a>; <a href="/?q=ut%3A%5C%28H_%5Cinfty%5C%29+performance+index">$H_\infty$ performance index</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 07470949" data-ciurl="/ci/07470949" data-biburl="/bibtex/07470949.bib" data-amsurl="/amsrefs/07470949.bib" data-xmlurl="/xml/07470949.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07470949.pdf" title="Zbl 07470949 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/10.1080/00207721.2019.1646349" aria-label="DOI for “Robust control synthesis for discrete-time uncertain semi-Markov jump systems”" title="10.1080/00207721.2019.1646349">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">Barbu, V.; Boussemart, M.; Limnios, N., Discrete-time semi-Markov model for reliability and survival analysis, Communications in Statistics Theory and Methods, 33, 11, 2833-2868 (2004) · <a href="/1089.60525" class="nowrap">Zbl 1089.60525</a> · <a href="https://doi.org/10.1081/STA-200037923" class="nowrap">doi:10.1081/STA-200037923</a></td> </tr><tr> <td>[2]</td> <td class="space">Barbu, V.; Limnios, N., Empirical estimation for discrete-time semi-Markov processes with applications in reliability, Nonparametric Statistics, 18, 7-8, 483-498 (2006) · <a href="/1117.62081" class="nowrap">Zbl 1117.62081</a> · <a href="https://doi.org/10.1080/10485250701261913" class="nowrap">doi:10.1080/10485250701261913</a></td> </tr><tr> <td>[3]</td> <td class="space">Barnes, A. 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