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By considering the properties of system output matrices, a method for \(H_{\infty }\) SOF control synthesis is developed in terms of solutions to a set of Linear Matrix Inequalities (LMIs). In contrast to the existing techniques for designing SOF controllers, the new proposed method can give less conservative results by removing the constraint that the considered Lyapunov matrix is diagonal. Numerical examples are given to illustrate the effectiveness of the proposed design method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5643655">Cited in <strong>27</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%3A93B35" title="MSC2020">93B35</a> </td> <td class="space"> Sensitivity (robustness) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A15A39" title="MSC2020">15A39</a> </td> <td class="space"> Linear inequalities of matrices </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%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B50" title="MSC2020">93B50</a> </td> <td class="space"> Synthesis problems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afuzzy+control">fuzzy control</a>; <a href="/?q=ut%3ATakagi-Sugeno+%28T-S%29+fuzzy+models">Takagi-Sugeno (T-S) fuzzy models</a>; <a href="/?q=ut%3A%5C%28H_%7B%5Cinfty+%7D%5C%29+control">\(H_{\infty }\) control</a>; <a href="/?q=ut%3Astatic+output+feedback">static output feedback</a>; <a href="/?q=ut%3Alinear+matrix+inequalities+%28LMIs%29">linear matrix inequalities (LMIs)</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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">&times;</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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1176.93044" data-ciurl="/ci/05643655" data-biburl="/bibtex/05643655.bib" data-amsurl="/amsrefs/05643655.bib" data-xmlurl="/xml/05643655.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05643655.pdf" title="Zbl 1176.93044 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.fss.2008.11.025" aria-label="DOI for “Static output feedback \(H_{\infty }\) control of a class of nonlinear discrete-time systems”" title="10.1016/j.fss.2008.11.025">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">Choi, D. 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C.M.; Assuncao, E.; Avellar, R. G., On relaxed LMI-based designs for fuzzy regulators and fuzzy observers, IEEE Transactions on Fuzzy Systems, 11, 5, 613-623 (2003)</td> </tr><tr> <td>[27]</td> <td class="space">Tseng, C.-S.; Hwang, C.-K., Fuzzy observer-based fuzzy control design for nonlinear systems with persistent bounded disturbances, Fuzzy Sets and Systems, 158, 2, 164-179 (2007) &middot; <a href="/1110.93032" class="nowrap">Zbl 1110.93032</a></td> </tr><tr> <td>[28]</td> <td class="space">Tuan, H. 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H., Output feedback \(H_\infty\) control of systems with parameter uncertainty, International Journal of Control, 63, 4, 741-750 (1996) &middot; <a href="/0841.93014" class="nowrap">Zbl 0841.93014</a></td> </tr><tr> <td>[31]</td> <td class="space">Yoneyama, J., Robust \(H_\infty\) control analysis and synthesis for Takagi-Sugeno general uncertain fuzzy systems, Fuzzy Sets and Systems, 157, 16, 2205-2223 (2006) &middot; <a href="/1106.93038" class="nowrap">Zbl 1106.93038</a></td> </tr><tr> <td>[32]</td> <td class="space">Zhou, S.; Feng, G.; Lam, J.; Xu, S., Robust \(H_\infty\) control for discrete-time fuzzy systems via basis-dependent Lyapunov functions, Information Sciences, 174, 3-4, 197-217 (2005) &middot; <a href="/1113.93038" class="nowrap">Zbl 1113.93038</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&nbsp;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"> &copy; 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 &amp; 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">&nbsp;<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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