Document Zbl 1305.93120

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J. Syst. Sci.</a> <a href="/?q=in%3A310215" title="Articles in this Issue">43, No. 12, 2249-2260 (2012)</a>. </div> <div class="abstract">Summary: The problem of robust $H_\infty$ control for uncertain discrete-time Takagi and Sugeno (T-S) fuzzy networked control systems (NCSs) with state quantisation is investigated. A new model of network-based control with simultaneous consideration of network-induced delays and packet dropouts is proposed. By using a fuzzy Lyapunov-Krasovskii functional (LKF), we derive a less conservative delay-dependent stability condition for the closed-loop NCSs. Robust $H_\infty$ fuzzy controller is developed for the asymptotical stabilisation of the NCSs. Since it is not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. A numerical example shows the feasibility applications of the proposed technique.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6382322">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C42" title="MSC2020">93C42</a> </td> <td class="space"> Fuzzy control/observation 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> <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%3A93B35" title="MSC2020">93B35</a> </td> <td class="space"> Sensitivity (robustness) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anetworked+%5C%28H_%5Cinfty%5C%29+control">networked $H_\infty$ control</a>; <a href="/?q=ut%3Afuzzy+system">fuzzy system</a>; <a href="/?q=ut%3Atime-varying+delay">time-varying delay</a>; <a href="/?q=ut%3Alinear+matrix+inequality">linear matrix inequality</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" 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class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1080/00207721.2011.569672" aria-label="DOI for “Robust $H_\infty$ networked control for discrete-time fuzzy systems with state quantisation”" title="10.1080/00207721.2011.569672">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">DOI: 10.1109/91.842153 · <a href="https://doi.org/10.1109/91.842153" class="nowrap">doi:10.1109/91.842153</a></td> </tr><tr> <td>[2]</td> <td class="space">Chen S, Fuzzy Sets and Systems 13 pp 263– (2005) · <a href="https://doi.org/10.1109/TFUZZ.2004.839673" class="nowrap">doi:10.1109/TFUZZ.2004.839673</a></td> </tr><tr> <td>[3]</td> <td class="space">DOI: 10.1109/TFUZZ.2009.2014223 · <a href="https://doi.org/10.1109/TFUZZ.2009.2014223" class="nowrap">doi:10.1109/TFUZZ.2009.2014223</a></td> </tr><tr> <td>[4]</td> <td class="space">DOI: 10.1109/TSP.2009.2038965 · <a href="/1392.94183" class="nowrap">Zbl 1392.94183</a> · <a href="https://doi.org/10.1109/TSP.2009.2038965" class="nowrap">doi:10.1109/TSP.2009.2038965</a></td> </tr><tr> <td>[5]</td> <td class="space">DOI: 10.1109/TFUZZ.2010.2047648 · <a href="https://doi.org/10.1109/TFUZZ.2010.2047648" class="nowrap">doi:10.1109/TFUZZ.2010.2047648</a></td> </tr><tr> <td>[6]</td> <td class="space">DOI: 10.1109/9.618250 · <a href="/0887.93017" class="nowrap">Zbl 0887.93017</a> · <a href="https://doi.org/10.1109/9.618250" class="nowrap">doi:10.1109/9.618250</a></td> </tr><tr> <td>[7]</td> <td class="space">DOI: 10.1109/TAC.2005.858689 · <a href="/1365.81064" class="nowrap">Zbl 1365.81064</a> · <a href="https://doi.org/10.1109/TAC.2005.858689" class="nowrap">doi:10.1109/TAC.2005.858689</a></td> </tr><tr> <td>[8]</td> <td class="space">DOI: 10.1016/j.automatica.2007.06.015 · <a href="/1283.93131" class="nowrap">Zbl 1283.93131</a> · <a href="https://doi.org/10.1016/j.automatica.2007.06.015" class="nowrap">doi:10.1016/j.automatica.2007.06.015</a></td> </tr><tr> <td>[9]</td> <td class="space">DOI: 10.1016/j.automatica.2007.04.020 · <a href="/1138.93375" class="nowrap">Zbl 1138.93375</a> · <a href="https://doi.org/10.1016/j.automatica.2007.04.020" class="nowrap">doi:10.1016/j.automatica.2007.04.020</a></td> </tr><tr> <td>[10]</td> <td class="space">DOI: 10.1016/j.cam.2006.07.027 · <a href="/1136.93030" class="nowrap">Zbl 1136.93030</a> · <a href="https://doi.org/10.1016/j.cam.2006.07.027" class="nowrap">doi:10.1016/j.cam.2006.07.027</a></td> </tr><tr> <td>[11]</td> <td class="space">DOI: 10.1109/TFUZZ.2004.825085 · <a href="/1142.93363" class="nowrap">Zbl 1142.93363</a> · <a href="https://doi.org/10.1109/TFUZZ.2004.825085" class="nowrap">doi:10.1109/TFUZZ.2004.825085</a></td> </tr><tr> <td>[12]</td> <td class="space">DOI: 10.1049/iet-cta:20070015 · <a href="https://doi.org/10.1049/iet-cta:20070015" class="nowrap">doi:10.1049/iet-cta:20070015</a></td> </tr><tr> <td>[13]</td> <td class="space">DOI: 10.1109/TFUZZ.2008.917293 · <a href="https://doi.org/10.1109/TFUZZ.2008.917293" class="nowrap">doi:10.1109/TFUZZ.2008.917293</a></td> </tr><tr> <td>[14]</td> <td class="space">Mastellone, S, Abdallah, T and Dorato, P. 2005. Model-based Networked Control for Nonlinear Systems with Stochastic Packet Dropout. Process of American Control Conference. 2005. pp.2365–2370.</td> </tr><tr> <td>[15]</td> <td class="space">DOI: 10.1080/00207170110067116 · <a href="/1023.93055" class="nowrap">Zbl 1023.93055</a> · <a href="https://doi.org/10.1080/00207170110067116" class="nowrap">doi:10.1080/00207170110067116</a></td> </tr><tr> <td>[16]</td> <td class="space">DOI: 10.1016/j.automatica.2007.02.022 · <a href="/1120.93043" class="nowrap">Zbl 1120.93043</a> · <a href="https://doi.org/10.1016/j.automatica.2007.02.022" class="nowrap">doi:10.1016/j.automatica.2007.02.022</a></td> </tr><tr> <td>[17]</td> <td class="space">Park, P, Lee, S and Choi, D. 2003. State-feedback Stabilisation for Nonlinear Time-delay Systems: A New Fuzzy Weighting-dependent Lyapunov–Krasovskii Functional Approach. IEEE Conference on Decision and Control. 2003. pp.5233–5238.</td> </tr><tr> <td>[18]</td> <td class="space">DOI: 10.1016/j.ins.2007.05.025 · <a href="/1126.93338" class="nowrap">Zbl 1126.93338</a> · <a href="https://doi.org/10.1016/j.ins.2007.05.025" class="nowrap">doi:10.1016/j.ins.2007.05.025</a></td> </tr><tr> <td>[19]</td> <td class="space">Shen B, Automatica 17 pp 440– (2009)</td> </tr><tr> <td>[20]</td> <td class="space">DOI: 10.1109/91.481840 · <a href="https://doi.org/10.1109/91.481840" class="nowrap">doi:10.1109/91.481840</a></td> </tr><tr> <td>[21]</td> <td class="space">DOI: 10.1016/j.ins.2008.01.019 · <a href="/1179.93096" class="nowrap">Zbl 1179.93096</a> · <a href="https://doi.org/10.1016/j.ins.2008.01.019" class="nowrap">doi:10.1016/j.ins.2008.01.019</a></td> </tr><tr> <td>[22]</td> <td class="space">Tian, E, Yue, D, Zhang, Y and Chen, P. 2008b. Improved Stability Analysis for Discrete System with Interval Time-varying Delay. Proceedings of the 27th Chinese Control Conference. 2008b. pp.86–90. · <a href="https://doi.org/10.1109/CHICC.2008.4605399" class="nowrap">doi:10.1109/CHICC.2008.4605399</a></td> </tr><tr> <td>[23]</td> <td class="space">DOI: 10.1109/37.898792 · <a href="https://doi.org/10.1109/37.898792" class="nowrap">doi:10.1109/37.898792</a></td> </tr><tr> <td>[24]</td> <td class="space">Wu H, IEEE Transactions on Fuzzy Systems 36 pp 954– (2006)</td> </tr><tr> <td>[25]</td> <td class="space">DOI: 10.1109/TAC.2007.900839 · <a href="/1366.93215" class="nowrap">Zbl 1366.93215</a> · <a href="https://doi.org/10.1109/TAC.2007.900839" class="nowrap">doi:10.1109/TAC.2007.900839</a></td> </tr><tr> <td>[26]</td> <td class="space">DOI: 10.1109/TFUZZ.2006.889963 · <a href="https://doi.org/10.1109/TFUZZ.2006.889963" class="nowrap">doi:10.1109/TFUZZ.2006.889963</a></td> </tr><tr> <td>[27]</td> <td class="space">DOI: 10.1049/iet-cta.2008.0242 · <a href="https://doi.org/10.1049/iet-cta.2008.0242" class="nowrap">doi:10.1049/iet-cta.2008.0242</a></td> </tr><tr> <td>[28]</td> <td class="space">DOI: 10.1109/TFUZZ.2004.839661 · <a href="https://doi.org/10.1109/TFUZZ.2004.839661" class="nowrap">doi:10.1109/TFUZZ.2004.839661</a></td> </tr><tr> <td>[29]</td> <td class="space">DOI: 10.1016/j.automatica.2004.12.011 · <a href="/1091.93007" class="nowrap">Zbl 1091.93007</a> · <a href="https://doi.org/10.1016/j.automatica.2004.12.011" class="nowrap">doi:10.1016/j.automatica.2004.12.011</a></td> </tr><tr> <td>[30]</td> <td class="space">DOI: 10.1049/ip-cta:20050294 · <a href="https://doi.org/10.1049/ip-cta:20050294" class="nowrap">doi:10.1049/ip-cta:20050294</a></td> </tr><tr> <td>[31]</td> <td class="space">DOI: 10.1016/S1004-4132(06)60030-3 · <a href="/1173.93355" class="nowrap">Zbl 1173.93355</a> · <a href="https://doi.org/10.1016/S1004-4132(06)60030-3" class="nowrap">doi:10.1016/S1004-4132(06)60030-3</a></td> </tr><tr> <td>[32]</td> <td class="space">DOI: 10.1109/TFUZZ.2007.905921 · <a href="https://doi.org/10.1109/TFUZZ.2007.905921" class="nowrap">doi:10.1109/TFUZZ.2007.905921</a></td> </tr><tr> <td>[33]</td> <td class="space">Zhang H, Applications and Reviews 37 pp 160– (2007)</td> </tr><tr> <td>[34]</td> <td class="space">DOI: 10.1109/TAC.2007.904284 · <a href="/1366.93543" class="nowrap">Zbl 1366.93543</a> · <a href="https://doi.org/10.1109/TAC.2007.904284" class="nowrap">doi:10.1109/TAC.2007.904284</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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