Document Zbl 1283.93284

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The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed $H_\infty$ disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô’s differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6271363">Cited in <strong>149</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E11" title="MSC2020">93E11</a> </td> <td class="space"> Filtering in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60H10" title="MSC2020">60H10</a> </td> <td class="space"> Stochastic ordinary differential equations (aspects of stochastic analysis) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D30" title="MSC2020">93D30</a> </td> <td class="space"> Lyapunov and storage functions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AIt%C3%B4+stochastic+system">Itô stochastic system</a>; <a href="/?q=ut%3A%5C%28H_%5Cinfty%5C%29+filtering">$H_\infty$ filtering</a>; <a href="/?q=ut%3Arobust+filtering">robust filtering</a>; <a href="/?q=ut%3Anonlinear+filtering">nonlinear filtering</a>; <a href="/?q=ut%3Atime+delays">time delays</a>; <a href="/?q=ut%3ALyapunov-Krasovskii+functional">Lyapunov-Krasovskii functional</a>; <a href="/?q=ut%3Alinear+matrix+inequality">linear matrix inequality</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 1283.93284" data-ciurl="/ci/06271363" data-biburl="/bibtex/06271363.bib" data-amsurl="/amsrefs/06271363.bib" data-xmlurl="/xml/06271363.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06271363.pdf" title="Zbl 1283.93284 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.2007.09.016" aria-label="DOI for “$H_\infty$ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities”" title="10.1016/j.automatica.2007.09.016">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://bura.brunel.ac.uk/handle/2438/4923" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Anderson, B. 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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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