Document Zbl 0825.93169

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<a href="/authors/gahinet.pascal-m" title="Author Profile">Gahinet, Pascal</a>; <a href="/authors/becker.greg" title="Author Profile">Becker, Greg</a></div> <h2 class="title"> <strong>Self-scheduled ${\mathcal H}_ \infty$ control of linear parameter-varying systems: A design example.</strong> <i>(English)</i> <a class="label nowrap" href="/0825.93169">Zbl 0825.93169</a> </h2> <div class="source"> <a href="/serials/348" title="Journal Profile">Automatica</a> <a href="/?q=in%3A28293" title="Articles in this Issue">31, No. 9, 1251-1261 (1995)</a>. </div> <div class="abstract"></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A806664">Cited in <strong>172</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%3A93B35" title="MSC2020">93B35</a> </td> <td class="space"> Sensitivity (robustness) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C95" title="MSC2020">93C95</a> </td> <td class="space"> Application models in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B51" title="MSC2020">93B51</a> </td> <td class="space"> Design techniques (robust design, computer-aided design, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atime-dependent">time-dependent</a></div> <div class="software"> <h3>Software:</h3><a href="/software/6383">LMI toolbox</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 0825.93169" data-ciurl="/ci/00806664" data-biburl="/bibtex/00806664.bib" data-amsurl="/amsrefs/00806664.bib" data-xmlurl="/xml/00806664.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00806664.pdf" title="Zbl 0825.93169 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/10.1016/0005-1098(95)00038-X" aria-label="DOI for “Self-scheduled ${\mathcal H}_ \infty$ control of linear parameter-varying systems: A design example”" title="10.1016/0005-1098(95)00038-X">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">Apkarian, P.; Gahinet, P., A convex characterization of gain-scheduled $H_∞$ controllers, IEEE Trans. Autom. Control, AC-40 (1995) · <a href="/0826.93028" class="nowrap">Zbl 0826.93028</a></td> </tr><tr> <td>[2]</td> <td class="space">Arzelier, D.; Bernussou, J.; Garcia, J. M., About quadratic stabilizability of generalized linear systems, (Proc. 30th Conf. on Decision and Control. Proc. 30th Conf. on Decision and Control, Brighton, U.K. (1991)), 914-920</td> </tr><tr> <td>[3]</td> <td class="space">Barmish, B. R., Stabilization of uncertain systems via linear control, IEEE Trans. Autom. Control, AC-27, 848-850 (1982) · <a href="/0554.93054" class="nowrap">Zbl 0554.93054</a></td> </tr><tr> <td>[4]</td> <td class="space">Barmish, B. R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain linear system, J. Optim. Theory Applic., 46, 399-408 (1985) · <a href="/0549.93045" class="nowrap">Zbl 0549.93045</a></td> </tr><tr> <td>[5]</td> <td class="space">Becker, G.; Packard, A.; Philbrick, D.; Balas, G., Control of parametrically-dependent linear systems: a single quadratic Lyapunov approach, (Proc. American Control Conf.. Proc. American Control Conf., San Francisco, CA (1993)), 2795-2799</td> </tr><tr> <td>[6]</td> <td class="space">Boyd, S.; ElGhaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory, (SIAM Studies in Applied Mathematics, Vol. 15 (1994), SIAM: SIAM Philadelphia) · <a href="/0816.93004" class="nowrap">Zbl 0816.93004</a></td> </tr><tr> <td>[7]</td> <td class="space">Gahinet, P.; Apkarian, P., A linear matrix inequality approach to $H_∞$ control, Int. J. Robust and Nonlinear Control, 4, 421-448 (1994) · <a href="/0808.93024" class="nowrap">Zbl 0808.93024</a></td> </tr><tr> <td>[8]</td> <td class="space">Gahinet, P.; Nemirovski, A., General-purpose LMI solvers with benchmarks, (Proc. 32nd IEEE Conf. on Decision and Control. Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX (1993)), 3162-3165</td> </tr><tr> <td>[9]</td> <td class="space">Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M., (LMI Control Toolbox (1995), MathWorks Inc: MathWorks Inc Natick, MA)</td> </tr><tr> <td>[10]</td> <td class="space">Gahinet, P., Explicit controller formulas for LMI-based $H_∞$ synthesis, (Proc. American Control Conf.. Proc. American Control Conf., Baltimore, MD (1994)), 2396-2400 · <a href="/1129.83335" class="nowrap">Zbl 1129.83335</a></td> </tr><tr> <td>[11]</td> <td class="space">Nesterov, Y. E.; Nemirovski, A. S., Interior Point Polynomial Methods in Convex Programming: Theory and Applications, (SIAM Studies in Applied Mathematics, Vol. 13 (1994), SIAM: SIAM Philadelphia) · <a href="/0824.90112" class="nowrap">Zbl 0824.90112</a></td> </tr><tr> <td>[12]</td> <td class="space">Packard, A., Gain scheduling via linear fractional transformations, Syst. Control Lett., 22, 79-92 (1994) · <a href="/0792.93043" class="nowrap">Zbl 0792.93043</a></td> </tr><tr> <td>[13]</td> <td class="space">Packard, A.; Becker, G., Quadratic stabilization of parametrically-dependent linear systems using parametrically-dependent linear, dynamic feedback, Adv. Robust and Nonlinear Control Syst. DSC, 43, 29-36 (1992)</td> </tr><tr> <td>[14]</td> <td class="space">Packard, A.; Zhou, K.; Pandey, P.; Becker, G., A collection of robust control problems leading to LMIs, (Proc. 30th IEEE Conf. on Decision and Control. Proc. 30th IEEE Conf. on Decision and Control, Brighton, U.K. (1991)), 1245-1250</td> </tr><tr> <td>[15]</td> <td class="space">Packard, A.; Pandey, P.; Leonhardson, J.; Balas, G., Optimal, constant I/O similarity scaling for full-information and state-feedback control problems, Syst. Control Lett., 19, 271-280 (1992) · <a href="/0772.49021" class="nowrap">Zbl 0772.49021</a></td> </tr><tr> <td>[16]</td> <td class="space">Petersen, I. R., Notions of stabilizability and controllability for a class of uncertain linear systems, Int. J. Control, 46, 409-422 (1987) · <a href="/0625.93010" class="nowrap">Zbl 0625.93010</a></td> </tr><tr> <td>[17]</td> <td class="space">Ravi, R.; Nagpal, R. M.; Khargonekar, P. P., $H_∞$ control of linear time-varying systems: a state-space approach, SIAM J. Control Optim., 29, 1394-1413 (1991) · <a href="/0741.93017" class="nowrap">Zbl 0741.93017</a></td> </tr><tr> <td>[18]</td> <td class="space">Shamma, J. F.; Athans, M., Gain scheduling: potential hazards and possible remedies, (Proc. American Control Conf.. Proc. American Control Conf., Boston, MA (1991)), 516-521</td> </tr><tr> <td>[19]</td> <td class="space">Shamma, J. F.; Athans, M., Guaranteed properties of gain scheduled control for linear parameter-varying plants, Automatica, 27, 559-564 (1991) · <a href="/0754.93022" class="nowrap">Zbl 0754.93022</a></td> </tr><tr> <td>[20]</td> <td class="space">Shamma, J. F.; Cloutier, J. R., A linear parameter-varying approach to gain scheduled missile autopilot design, (Proc. American Control Conf.. Proc. American Control Conf., Chicago, IL (1992)), 1317-1321</td> </tr><tr> <td>[21]</td> <td class="space">Zhou, K.; Khargonekar, P. P.; Stoustrup, J.; Niemann, H. H., Robust stability and performance of uncertain systems in state space, (Proc. 31st IEEE Conf. on Decision and Control. Proc. 31st IEEE Conf. on Decision and Control, Tucson, AZ (1992)), 662-667</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. 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