Document Zbl 1091.93020

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The main contribution in this paper is that a new $\varepsilon$-independent controller is derived by solving the reduced-order slow and fast algebraic Riccati equations (AREs) whose dimension is smaller than the dimension of a full-order multiparameter algebraic Riccati equation (MARE). It is shown that if these AREs have a positive definite stabilizing solution then the closed-loop system is quadratically stable and has the cost bound.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5003081">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%3A93C70" title="MSC2020">93C70</a> </td> <td class="space"> Time-scale analysis and singular perturbations in control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C41" title="MSC2020">93C41</a> </td> <td class="space"> Control/observation systems with incomplete information </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amultiparameter+singularly+perturbed+systems+%28msps%29">multiparameter singularly perturbed systems (msps)</a>; <a href="/?q=ut%3Amultiparameter+algebraic+Riccati+equation+MARE">multiparameter algebraic Riccati equation MARE</a>; <a href="/?q=ut%3Auncertainty">uncertainty</a>; <a href="/?q=ut%3Aguaranteed+cost+control">guaranteed cost control</a>; <a href="/?q=ut%3A%5C%28%5Cvarepsilon%5C%29-independent+controller">$\varepsilon$-independent 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 1091.93020" data-ciurl="/ci/05003081" data-biburl="/bibtex/05003081.bib" data-amsurl="/amsrefs/05003081.bib" data-xmlurl="/xml/05003081.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05003081.pdf" title="Zbl 1091.93020 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.automatica.2005.01.003" aria-label="DOI for “A new approach to robust guaranteed cost control for uncertain multimodeling systems”" title="10.1016/j.automatica.2005.01.003">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">Corless, M.; Garofalo, F.; Glielmo, L., New results on composite control of singularly perturbed uncertain linear systems, Automatica, 29, 2, 387-400 (1993) · <a href="/0772.93062" class="nowrap">Zbl 0772.93062</a></td> </tr><tr> <td>[2]</td> <td class="space">Coumarbatch, C.; Gajić, Z., Exact decomposition of the algebraic Riccati equation of deterministic multimodeling optimal control problems, IEEE Transactions on Automatic Control, 45, 4, 790-794 (2000) · <a href="/0977.93052" class="nowrap">Zbl 0977.93052</a></td> </tr><tr> <td>[3]</td> <td class="space">Gajić, Z., The existence of a unique and bounded solution of the algebraic Riccati equation of multimodel estimation and control problems, Systems and Control Letters, 10, 185-190 (1988) · <a href="/0658.93018" class="nowrap">Zbl 0658.93018</a></td> </tr><tr> <td>[4]</td> <td class="space">Gajić, Z.; Khalil, H. K., Multimodel strategies under random disturbances and imperfect partial observations, Automatica, 22, 1, 121-125 (1986) · <a href="/0585.93005" class="nowrap">Zbl 0585.93005</a></td> </tr><tr> <td>[5]</td> <td class="space">Gajić, Z.; Petkovski, D.; Harkara, N., The recursive algorithm for the optimal static output feedback control problem of linear singularity perturbed systems, IEEE Transactions on Automatic Control, 34, 4, 465-468 (1989) · <a href="/0666.93031" class="nowrap">Zbl 0666.93031</a></td> </tr><tr> <td>[6]</td> <td class="space">Khalil, H. K., Stabilization of multiparameter singularly perturbed systems, IEEE Transactions on Automatic Control, 24, 5, 790-791 (1979) · <a href="/0416.93074" class="nowrap">Zbl 0416.93074</a></td> </tr><tr> <td>[7]</td> <td class="space">Khalil, H. K., On the robustness of output feedback control methods to modeling errors, IEEE Transactions on Automatic Control, 26, 2, 524-526 (1981) · <a href="/0474.93024" class="nowrap">Zbl 0474.93024</a></td> </tr><tr> <td>[8]</td> <td class="space">Khalil, H. K.; Kokotović, P. V., Control strategies for decision makers using different models of the same system, IEEE Transactions on Automatic Control, 23, 2, 289-298 (1978) · <a href="/0384.93007" class="nowrap">Zbl 0384.93007</a></td> </tr><tr> <td>[9]</td> <td class="space">Khalil, H. K.; Kokotović, P. V., Control of linear systems with multiparameter singular perturbations, Automatica, 15, 2, 197-207 (1979) · <a href="/0409.93019" class="nowrap">Zbl 0409.93019</a></td> </tr><tr> <td>[10]</td> <td class="space">Magnus, J. R.; Neudecker, H., Matrix differential calculus with applications in statistics and econometrics (1999), Wiley: Wiley New York · <a href="/0912.15003" class="nowrap">Zbl 0912.15003</a></td> </tr><tr> <td>[11]</td> <td class="space">Moheimani, S. O.R.; Petersen, I. R., Optimal guaranteed cost control of uncertain systems via static and dynamic output feedback, Automatica, 32, 4, 575-579 (1996) · <a href="/0855.93093" class="nowrap">Zbl 0855.93093</a></td> </tr><tr> <td>[12]</td> <td class="space">Mukaidani, H., An LMI approach to guaranteed cost control for uncertain delay systems, IEEE Transactions Circuits and Systems IFundamental Theory and Applications, 50, 6, 795-800 (2003) · <a href="/1368.93277" class="nowrap">Zbl 1368.93277</a></td> </tr><tr> <td>[13]</td> <td class="space">Mukaidani, H.; Mizukami, K., The guaranteed cost control problem of uncertain singularly perturbed systems, Journal of Mathematical Analysis and Applications, 251, 716-735 (2000) · <a href="/0976.93059" class="nowrap">Zbl 0976.93059</a></td> </tr><tr> <td>[14]</td> <td class="space">Mukaidani, H.; Shimomura, T.; Mizukami, K., Asymptotic expansions and new numerical algorithm of the algebraic Riccati equation for multiparameter singularly perturbed systems, Journal of Mathematical Analysis and Applications, 267, 209-234 (2002) · <a href="/1004.93031" class="nowrap">Zbl 1004.93031</a></td> </tr><tr> <td>[15]</td> <td class="space">Mukaidani, H.; Xu, H., $H_2$ guaranteed cost control problem of singularly perturbed systems with uncertainties, International Journal of Systems Sciences, 32, 12, 1333-1343 (2001) · <a href="/1039.93044" class="nowrap">Zbl 1039.93044</a></td> </tr><tr> <td>[16]</td> <td class="space">Mukaidani, H.; Xu, H.; Mizukami, K., Near-optimal control of linear multiparameter singularly perturbed systems, IEEE Transactions on Automatic Control, 47, 12, 2051-2057 (2002) · <a href="/1364.49029" class="nowrap">Zbl 1364.49029</a></td> </tr><tr> <td>[17]</td> <td class="space">Mukaidani, H.; Xu, H.; Mizukami, K., Near-optimal control of linear multiparameter singularly perturbed systems, Automatica, 39, 12, 2157-2167 (2003) · <a href="/1047.93034" class="nowrap">Zbl 1047.93034</a></td> </tr><tr> <td>[18]</td> <td class="space">Ortega, J. M., Numerical analysis, a second course (1990), SIAM: SIAM Philadelphia · <a href="/0701.65002" class="nowrap">Zbl 0701.65002</a></td> </tr><tr> <td>[19]</td> <td class="space">Pan, Z.; Basar, T., $H_\infty $-optimal control for singularly perturbed systems. Part IPerfect state measurements, Automatica, 29, 2, 401-423 (1993) · <a href="/0782.49015" class="nowrap">Zbl 0782.49015</a></td> </tr><tr> <td>[20]</td> <td class="space">Petersen, I. R.; McFarlane, D. C., Optimal guaranteed cost control and filtering for uncertain linear systems, IEEE Transactions on Automatic Control, 39, 9, 1971-1977 (1994) · <a href="/0817.93025" class="nowrap">Zbl 0817.93025</a></td> </tr><tr> <td>[21]</td> <td class="space">Ran, A. C.M.; Vreugdenhil, R., Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems, Linear Algebra and its Applications, 99, 63-83 (1988) · <a href="/0637.15008" class="nowrap">Zbl 0637.15008</a></td> </tr><tr> <td>[22]</td> <td class="space">Takaba, K.; Morihira, N.; Katayama, T., A generalized Lyapunov theorem for descriptor system, Systems and Control Letters, 24, 1, 49-51 (1995) · <a href="/0883.93035" class="nowrap">Zbl 0883.93035</a></td> </tr><tr> <td>[23]</td> <td class="space">Wang, Y.-Y.; Frank, P. M.; Wu, N. E., Near-optimal control of nonstandard singularly perturbed systems, Automatica, 30, 2, 277-292 (1994) · <a href="/0815.93052" class="nowrap">Zbl 0815.93052</a></td> </tr><tr> <td>[24]</td> <td class="space">Yu, L.; Chu, J., An LMI approach to guaranteed cost control of linear uncertain time delay systems, Automatica, 35, 6, 1155-1159 (1999) · <a href="/1041.93530" class="nowrap">Zbl 1041.93530</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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