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Control Signals Syst.</a> <a href="/?q=in%3A125969" title="Articles in this Issue">18, No. 2, 187-197 (2006)</a>. </div> <div class="abstract">Summary: Global asymptotic stability conditions for nonlinear stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of the system coefficients. Nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5076319">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%3A93E03" title="MSC2020">93E03</a> </td> <td class="space"> Stochastic systems in control theory (general) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D20" title="MSC2020">93D20</a> </td> <td class="space"> Asymptotic stability in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D05" title="MSC2020">93D05</a> </td> <td class="space"> Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AStochastic+time-delay+system">Stochastic time-delay system</a>; <a href="/?q=ut%3AAsymptotic+stability">Asymptotic stability</a>; <a href="/?q=ut%3AMartingale+convergence+theorems">Martingale convergence theorems</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">×</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 1103.93043" data-ciurl="/ci/05076319" data-biburl="/bibtex/05076319.bib" data-amsurl="/amsrefs/05076319.bib" data-xmlurl="/xml/05076319.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05076319.pdf" title="Zbl 1103.93043 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/10.1007/s00498-006-0163-1" aria-label="DOI for “On delay-dependent stability for a class of nonlinear stochastic delay-differential equations”" title="10.1007/s00498-006-0163-1">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">Boukas E-K, Liu Z-K (2002) Deterministic and stochastic time-delay systems. 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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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