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Franklin Inst.</a> <a href="/?q=in%3A335610" title="Articles in this Issue">351, No. 2, 1027-1041 (2014)</a>. </div> <div class="abstract">Summary: A novel control scheme combining disturbance observer technique and back-stepping method is proposed for a class of nonlinear system with multiple mismatched disturbances. The uncertain multiple mismatched disturbances contain not only single harmonic or constant disturbances but also another unexpected nonlinear signal presented as a nonlinear function. The composite adaptive disturbance observers are designed to estimate the disturbances with partial known information. By integrating disturbance observer based control with back-stepping method, a composite controller is designed. Here, the disturbance estimations are introduced into the design of virtual control laws in each step to compensate the mismatched disturbances. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in spite of existing multiple mismatched disturbances. Finally, a simulation example is applied to demonstrate the effectiveness of the proposed method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6330752">Cited in <strong>34</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B07" title="MSC2020">93B07</a> </td> <td class="space"> Observability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C40" title="MSC2020">93C40</a> </td> <td class="space"> Adaptive control/observation systems </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%3A93D15" title="MSC2020">93D15</a> </td> <td class="space"> Stabilization of systems by feedback </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%3Acomposite+adaptive+disturbance+observer+based+control">composite adaptive disturbance observer based control</a>; <a href="/?q=ut%3Aback-stepping+method">back-stepping method</a>; <a href="/?q=ut%3Anonlinear+system">nonlinear system</a>; <a href="/?q=ut%3Amultiple+mismatched+disturbances">multiple mismatched disturbances</a>; <a href="/?q=ut%3Astability+analysis">stability analysis</a>; <a href="/?q=ut%3Aclosed-loop+system">closed-loop system</a>; <a href="/?q=ut%3Adirect+Lyapunov+function+method">direct Lyapunov function method</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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">&times;</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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1293.93120" data-ciurl="/ci/06330752" data-biburl="/bibtex/06330752.bib" data-amsurl="/amsrefs/06330752.bib" data-xmlurl="/xml/06330752.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06330752.pdf" title="Zbl 1293.93120 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.jfranklin.2013.10.002" aria-label="DOI for “Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances”" title="10.1016/j.jfranklin.2013.10.002">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">ÅStróm, K. 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