Document Zbl 1482.93167

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J. Syst. Sci., Princ. Appl. Syst. Integr.</a> <a href="/?q=in%3A476082" title="Articles in this Issue">49, No. 5, 997-1011 (2018)</a>. </div> <div class="abstract">Summary: This paper investigates the $H_\infty$ control problem based on exponential stability and weighted $L_2$-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov-Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and $L_2$-gain analyses, sufficient delay-dependent exponential stability and weighted $L_2$-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an $H_\infty$ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7469637">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%3A93B36" title="MSC2020">93B36</a> </td> <td class="space"> $H^\infty$-control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D23" title="MSC2020">93D23</a> </td> <td class="space"> Exponential stability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B52" title="MSC2020">93B52</a> </td> <td class="space"> Feedback control </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%3A93C43" title="MSC2020">93C43</a> </td> <td class="space"> Delay control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aexponential+stability">exponential stability</a>; <a href="/?q=ut%3A%5C%28H_%5Cinfty%5C%29+control">$H_\infty$ control</a>; <a href="/?q=ut%3Aperiodic+piecewise+systems">periodic piecewise systems</a>; <a href="/?q=ut%3Atime+delay">time delay</a></div> <div class="software"> <h3>Software:</h3><a href="/software/5124">PENBMI</a>; <a href="/software/4595">YALMIP</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 1482.93167" data-ciurl="/ci/07469637" data-biburl="/bibtex/07469637.bib" data-amsurl="/amsrefs/07469637.bib" data-xmlurl="/xml/07469637.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07469637.pdf" title="Zbl 1482.93167 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/10.1080/00207721.2018.1440028" aria-label="DOI for “$H_\infty$ control problem of linear periodic piecewise time-delay systems”" title="10.1080/00207721.2018.1440028">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">Ai, Z.; Peng, L., Exponential stabilisation of impulsive switched linear systems via a periodic switching scheme, IET Control Theory & Applications,, 11, 16, 2921-2926 (2017)</td> </tr><tr> <td>[2]</td> <td class="space">Bittanti, S.; Colaneri, P., Periodic systems: Filtering and control (2008), London: Springer-Verlag, London</td> </tr><tr> <td>[3]</td> <td class="space">Cao, Y.-Y.; Lam, J.; Sun, Y.-X, Static output feedback stabilization: An ILMI approach, Automatica,, 34, 12, 1641-1645 (1998) · <a href="/0937.93039" class="nowrap">Zbl 0937.93039</a></td> </tr><tr> <td>[4]</td> <td class="space">Chen, Y.; Fei, S.; Li, Y., Robust stabilization for uncertain saturated time-delay systems: A distributed-delay-dependent polytopic approach, IEEE Transactions on Automatic Control, 62, 7, 3455-3460 (2017) · <a href="/1370.93231" class="nowrap">Zbl 1370.93231</a></td> </tr><tr> <td>[5]</td> <td class="space">Chen, Y.; Fei, S.; Zhang, K., Stabilisation for switched linear systems with time-varying delay and input saturation, International Journal of Systems Science,, 45, 3, 532-546 (2014) · <a href="/1307.93302" class="nowrap">Zbl 1307.93302</a></td> </tr><tr> <td>[6]</td> <td class="space">Ding, D.; Wang, Z.; Ho, D. 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