Document Zbl 1169.93323

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J. Robust Nonlinear Control</a> <a href="/?q=in%3A233830" title="Articles in this Issue">18, No. 18, 1657-1680 (2008)</a>. </div> <div class="abstract">Summary: General recent techniques in Fault Detection and Isolation (FDI) are based on $H_\infty$ optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed Linear Matrix Inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation-based design methods. This article presents an LMI formulation to design full-order and reduced-order robust $H_\infty$ FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full-order filter, which may be solved via recently developed LMI optimization techniques. For the reduced-order FDI filter, the inequalities include a non-convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5596430">Cited in <strong>19</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A93B36" title="MSC2020">93B36</a> </td> <td class="space"> $H^\infty$-control </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%3A93B50" title="MSC2020">93B50</a> </td> <td class="space"> Synthesis problems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C05" title="MSC2020">93C05</a> </td> <td class="space"> Linear systems in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afault+detection+and+isolation">fault detection and isolation</a>; <a href="/?q=ut%3Alinear+matrix+inequalities">linear matrix inequalities</a>; <a href="/?q=ut%3Arobust+%5C%28H_%5Cinfty%5C%29+filtering">robust $H_\infty$ filtering</a>; <a href="/?q=ut%3Alinear+systems">linear systems</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 1169.93323" data-ciurl="/ci/05596430" data-biburl="/bibtex/05596430.bib" data-amsurl="/amsrefs/05596430.bib" data-xmlurl="/xml/05596430.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05596430.pdf" title="Zbl 1169.93323 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/10.1002/rnc.1313" aria-label="DOI for “Robust fault estimation of uncertain systems using an LMI-based approach”" title="10.1002/rnc.1313">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">Beard RV. 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