Document Zbl 1329.93112

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The algorithm has two similar stages, where in the first one the feasibility problem is solved, and in the second one the optimization problem is solved. The formulation is unified for the feasibility and for the optimization problems, as well as for continuous-time or discrete-time systems. The method is demonstrated by applying it to the hard (conjectured to be NP-hard) problem of the minimal-gain static-output-stabilizing-feedback, and to the hard (conjectured to be NP-hard) problem of regional pole-placement via static-output-feedback in non-convex or unconnected regions. A proof of convergence (in probability) that captures the two rounds of the algorithm is given, and complexity analysis is provided, under some mild assumptions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6524067">Cited in <strong>12</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D15" title="MSC2020">93D15</a> </td> <td class="space"> Stabilization of systems by feedback </td> </tr><tr> <td class="mono"> 93B40 </td> <td class="space"> Computational methods in systems theory (MSC2010) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B52" title="MSC2020">93B52</a> </td> <td class="space"> Feedback control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B55" title="MSC2020">93B55</a> </td> <td class="space"> Pole and zero placement problems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alinear+systems">linear systems</a>; <a href="/?q=ut%3Astate-space+representation">state-space representation</a>; <a href="/?q=ut%3Afeedback-stability">feedback-stability</a>; <a href="/?q=ut%3Astatic+output+feedbacks">static output feedbacks</a>; <a href="/?q=ut%3Apole-placement">pole-placement</a>; <a href="/?q=ut%3Aapproximation+algorithms">approximation algorithms</a>; <a href="/?q=ut%3Arandomized+algorithms">randomized algorithms</a></div> <div class="software"> <h3>Software:</h3><a href="/software/15253">RICPAC</a>; <a href="/software/5124">PENBMI</a>; <a href="/software/5188">HIFOO</a>; <a href="/software/6359">COMPleib</a>; <a href="/software/149">complib</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 1329.93112" data-ciurl="/ci/06524067" data-biburl="/bibtex/06524067.bib" data-amsurl="/amsrefs/06524067.bib" data-xmlurl="/xml/06524067.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06524067.pdf" title="Zbl 1329.93112 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.2015.10.001" aria-label="DOI for “A randomized approximation algorithm for the minimal-norm static-output-feedback problem”" title="10.1016/j.automatica.2015.10.001">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[2]</td> <td class="space">Apkarian, P.; Noll, D., Nonsmooth $H_\infty$ synthesis, IEEE Transactions on Automatic Control, 51, 1, 7186 (2006) · <a href="/1366.93148" class="nowrap">Zbl 1366.93148</a></td> </tr><tr> <td>[3]</td> <td class="space">Arnold, W. 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