Document Zbl 1405.90100

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Control Optim.</a> <a href="/?q=in%3A413812" title="Articles in this Issue">56, No. 5, 3619-3641 (2018)</a>. </div> <div class="abstract">Summary: While sliding mode observers (SMOs) using discontinuous relays are widely analyzed, most SMOs are implemented computationally using a continuous approximation of the discontinuous relays. This results in the formation of a boundary layer in a neighborhood of the sliding manifold in the observer error space. In this paper, a convex programming method for constructing boundary-layer SMOs (BL-SMOs) is presented for a wide class of nonlinear systems characterized by incremental quadratic constraints. Specifically, the observer gains are computed by solving a set of linear matrix inequalities and ultimate bounds on the state of a synthetic descriptor system. A novel application of filtering using smooth window functions is leveraged to reconstruct the unknown exogenous inputs to prescribed accuracy. Two numerical examples are presented to illustrate the effectiveness of our proposed approach.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6950099">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C25" title="MSC2020">90C25</a> </td> <td class="space"> Convex programming </td> </tr><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%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%3Aunknown+input+observers">unknown input observers</a>; <a href="/?q=ut%3Alow-pass+filtering">low-pass filtering</a>; <a href="/?q=ut%3Aincremental+quadratic+constraints">incremental quadratic constraints</a>; <a href="/?q=ut%3Asliding+mode">sliding mode</a>; <a href="/?q=ut%3Adescriptor+systems">descriptor systems</a>; <a href="/?q=ut%3Amultiplier+matrix">multiplier matrix</a>; <a href="/?q=ut%3Alinear+matrix+inequalities">linear matrix inequalities</a></div> <div class="software"> <h3>Software:</h3><a href="/software/4594">CVX</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 1405.90100" data-ciurl="/ci/06950099" data-biburl="/bibtex/06950099.bib" data-amsurl="/amsrefs/06950099.bib" data-xmlurl="/xml/06950099.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06950099.pdf" title="Zbl 1405.90100 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/10.1137/16M1078793" aria-label="DOI for “Unknown input estimation for nonlinear systems using sliding mode observers and smooth window functions”" title="10.1137/16M1078793">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1507.03924"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">B. 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