Document Zbl 0875.93108

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K.</a>; <a href="/authors/jiang.weisun" title="Author Profile">Jiang, Weisun</a></div> <h2 class="title"> <strong>Robust $H_{\infty}$ control for linear discrete-time systems with norm-bounded time-varying uncertainty.</strong> <i>(English)</i> <a class="label nowrap" href="/0875.93108">Zbl 0875.93108</a> </h2> <div class="source"> <a href="/serials/870" title="Journal Profile">Syst. Control Lett.</a> <a href="/?q=in%3A33042" title="Articles in this Issue">27, No. 4, 199-208 (1996)</a>. </div> <div class="abstract">Summary: The problem of robust $H_{\infty}$ analysis and synthesis for linear discrete-time systems with norm-bounded time-varying uncertainty is studied in this paper. It will be shown that this problem is equivalent to the problem of $H_{\infty}$ analysis and synthesis of an auxiliary system. The necessary and sufficient conditions for the equivalency are proved. Thus the original problem can be solved by existing $H_{\infty}$ control methods.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A984381">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A984381">Cited in <strong>18</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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3A%5C%28H_%7B%5Cinfty%7D%5C%29+control">$H_{\infty}$ control</a>; <a href="/?q=ut%3AUncertain+system">Uncertain system</a>; <a href="/?q=ut%3ARobust+control">Robust control</a>; <a href="/?q=ut%3ADiscrete-time+system">Discrete-time system</a>; <a href="/?q=ut%3ATime-varying+uncertainty">Time-varying uncertainty</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 0875.93108" data-ciurl="/ci/00984381" data-biburl="/bibtex/00984381.bib" data-amsurl="/amsrefs/00984381.bib" data-xmlurl="/xml/00984381.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00984381.pdf" title="Zbl 0875.93108 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/10.1016/0167-6911(95)00049-6" aria-label="DOI for “Robust $H_{\infty}$ control for linear discrete-time systems with norm-bounded time-varying uncertainty”" title="10.1016/0167-6911(95)00049-6">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">Barmish, B. R., Necessary and sufficient conditions for quadratic stabilizibility of an uncertain system, J. Opt. Theory Appl., 46, 399-408 (1985) · <a href="/0549.93045" class="nowrap">Zbl 0549.93045</a></td> </tr><tr> <td>[2]</td> <td class="space">de Souza, C. E.; Fu, M.; Xie, L., $H_∞$ analysis and synthesis of discrete-time systems with time-varying uncertainty, IEEE Trans. Automat. Control, AC-38, 459-462 (1993) · <a href="/0791.93064" class="nowrap">Zbl 0791.93064</a></td> </tr><tr> <td>[3]</td> <td class="space">Doyle, J. C., Analysis of feedback systems with structured uncertainties, (IEE Proc., 129 (1982)), 242-250, Part D</td> </tr><tr> <td>[4]</td> <td class="space">Francis, B. A., A Course in $H_∞$ Control Theory (1987), Springer: Springer New York · <a href="/0624.93003" class="nowrap">Zbl 0624.93003</a></td> </tr><tr> <td>[5]</td> <td class="space">Furuta, K.; Phoojaruenchanachai, S., An algebraic approach to discrete-time $H_∞$ control problems, (Proc. 1990 Amer. Contr. Conf.. Proc. 1990 Amer. Contr. Conf., San Diego, CA (May 1990))</td> </tr><tr> <td>[6]</td> <td class="space">Garcia, G.; Bernussou, J.; Arzelier, D., Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty, Systems Control Lett., 22, 327-339 (1994) · <a href="/0820.93059" class="nowrap">Zbl 0820.93059</a></td> </tr><tr> <td>[7]</td> <td class="space">Haddad, W. M.; Huang, H.; Bernstein, D. S., Robust stability and performance via fixed-order dynamic compensation: the discrete-time case, IEEE Trans. Automat. Control, AC-38, 776-782 (1993) · <a href="/0785.93073" class="nowrap">Zbl 0785.93073</a></td> </tr><tr> <td>[8]</td> <td class="space">Ionescu, V.; Weiss, M., Two Riccati formulatae for the discrete-time $H_∞$ control problem, Int. J. Control, 57, 141-196 (1993) · <a href="/0774.93026" class="nowrap">Zbl 0774.93026</a></td> </tr><tr> <td>[9]</td> <td class="space">Khargonekar, P. P.; Petersen, I. R.; Rotea, M. A., $H_∞$ optimal control with state feedback, IEEE Trans. Automat. Control, AC-33, 786-788 (1998) · <a href="/0655.93026" class="nowrap">Zbl 0655.93026</a></td> </tr><tr> <td>[10]</td> <td class="space">Khargonekar, P. P.; Petersen, I. R.; Zhou, K., Robust stabilization of uncertain linear system: quadratic stabilizability and $H_∞$ control theory, IEEE Trans. Automat. Control, AC-35, 356-361 (1990) · <a href="/0707.93060" class="nowrap">Zbl 0707.93060</a></td> </tr><tr> <td>[11]</td> <td class="space">Limebeer, D. J.N.; Green, M.; Walker, D., Discrete time $H_∞$ control, (Proc. 28th Conf. on Deci. Contr.. Proc. 28th Conf. on Deci. Contr., Tampa, FL (1989)), 392-396</td> </tr><tr> <td>[12]</td> <td class="space">Magana, M. E.; Zak, S. H., Robust state feedback stabilization of discrete-time uncertain dynamically systems, IEEE Trans. Automat. Control, AC-33, 887-891 (1988) · <a href="/0663.93054" class="nowrap">Zbl 0663.93054</a></td> </tr><tr> <td>[13]</td> <td class="space">Magana, M. E.; Zak, S. H., Robust output feedback stabilization of discrete-time uncertain dynamical systems, IEEE Trans. Automat. Control, AC-33, 1082-1085 (1988) · <a href="/0655.93058" class="nowrap">Zbl 0655.93058</a></td> </tr><tr> <td>[14]</td> <td class="space">Petersen, I. R.; Hollot, C. V., A Riccati equation approach to the stabilization of uncertain linear system, Automatica, 22, 397-411 (1986) · <a href="/0602.93055" class="nowrap">Zbl 0602.93055</a></td> </tr><tr> <td>[15]</td> <td class="space">Sampei; Mita, T.; Nakamichi, M., An algebraic approach to the $H_∞$ output feedback control problem, Systems Control Lett., 14, 13-24 (1990) · <a href="/0692.93031" class="nowrap">Zbl 0692.93031</a></td> </tr><tr> <td>[16]</td> <td class="space">Stoorvogel, A. A.; Weeren, A. J.T. M., The discrete-time Riccati equation related to the $H_∞$ control problem, IEEE Trans. Automat. Control, AC-39, 686-691 (1994) · <a href="/0815.93029" class="nowrap">Zbl 0815.93029</a></td> </tr><tr> <td>[17]</td> <td class="space">Xie, L.; de Souza, C. E., Robust $H_∞$ control for linear systems with norm-bounded time-varying uncertainty, IEEE Trans. Automat. Control, AC-37, 1188-1191 (1992) · <a href="/0764.93027" class="nowrap">Zbl 0764.93027</a></td> </tr><tr> <td>[18]</td> <td class="space">Xie, L.; Fu, M.; de Souza, C. E., $H_∞$ control and quadratic stabilization of systems with parameter uncertainty via output feedback, IEEE Trans. Automat. Control, AC-37, 1253-1256 (1992) · <a href="/0764.93067" class="nowrap">Zbl 0764.93067</a></td> </tr><tr> <td>[19]</td> <td class="space">Yaesh, I.; Shaked, V., $H_∞$ optimal one-step-ahead output feedback control of discrete time systems, IEEE Trans. Automat. Control, AC-37, 1245-1250 (1992) · <a href="/0769.93052" class="nowrap">Zbl 0769.93052</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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