Document Zbl 1433.93151

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Math. Comput.</a> <a href="/?q=in%3A444252" title="Articles in this Issue">369, Article ID 124834, 15 p. (2020)</a>. </div> <div class="abstract">Summary: This paper proposes some new sufficient conditions and necessary conditions for exponential mean stability with prescribed decay rate, and sufficient conditions for non-fragile controller design of both continuous-time and discrete-time positive Markov jump linear systems with time-delay. First, sufficient stability conditions are derived by constructing novel linear stochastic co-positive Lyapunov-Krasovskii functionals. Second, the corresponding necessary conditions are established by applying a model transformation technique and analyzing the relationship between stochastic stability of the transformed systems and exponential mean stability with given decay rate of the original systems. Compared with the existing conditions, the proposed stability conditions are not only delay-dependent but also decay-rate-dependent, and the sufficient conditions plus the necessary conditions can be used to judge the system stability more precisely. Third, based on the new sufficient conditions, non-fragile controllers are designed by solving linear programming problems such that the closed-loop systems are positive and exponentially mean stable with an expected decay rate. Finally, by numerical examples, the effects of both time-delay and decay rate on exponential mean stability are exploited and the validity of the non-fragile controller design conditions is demonstrated.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7154261">Cited in <strong>7</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%3A60J20" title="MSC2020">60J20</a> </td> <td class="space"> Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) </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%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apositive+Markov+jump+linear+systems">positive Markov jump linear systems</a>; <a href="/?q=ut%3Adecay-rate">decay-rate</a>; <a href="/?q=ut%3Atime-delay">time-delay</a>; <a href="/?q=ut%3Aexponential+mean+stability">exponential mean stability</a>; <a href="/?q=ut%3Anon-fragile+controller">non-fragile controller</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 1433.93151" data-ciurl="/ci/07154261" data-biburl="/bibtex/07154261.bib" data-amsurl="/amsrefs/07154261.bib" data-xmlurl="/xml/07154261.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07154261.pdf" title="Zbl 1433.93151 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.2019.124834" aria-label="DOI for “Delay-dependent and decay-rate-dependent conditions for exponential mean stability and non-fragile controller design of positive Markov jump linear systems with time-delay”" title="10.1016/j.amc.2019.124834">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">Farina, L.; Rinaldi, S., Positive Linear Systems: Theory and Applications (2000), Wiley: Wiley New York · <a href="/0988.93002" class="nowrap">Zbl 0988.93002</a></td> </tr><tr> <td>[2]</td> <td class="space">Kaczorek, T., Positive 1D and 2D systems (2002), Springer: Springer London · <a href="/1005.68175" class="nowrap">Zbl 1005.68175</a></td> </tr><tr> <td>[3]</td> <td class="space">Rami, M. 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