Document Zbl 1485.93611

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(2022)</a>. </div> <div class="abstract">Summary: A new concept of stabilisation of hybrid stochastic systems in distribution by feedback controls based on discrete-time state observations is initialised. This is to design a controller to stabilise the unstable system such that the distribution of the solution process tends to a probability distribution. In addition, the discrete-time state observations are also taken into consideration to make the design of the controller more practical. Theorems on the stabilisation of hybrid stochastic systems in distribution are proved. The lower bound of the duration between two consecutive state observations is obtained. The implementation of theorems are demonstrated by designing the feedback controls in the structure cases and easy-to-rules are provided for the user. Numerical examples are discussed to illustrate the theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7507277">Cited in <strong>14</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E15" title="MSC2020">93E15</a> </td> <td class="space"> Stochastic stability 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%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C30" title="MSC2020">93C30</a> </td> <td class="space"> Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60H30" title="MSC2020">60H30</a> </td> <td class="space"> Applications of stochastic analysis (to PDEs, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ABrownian+motion">Brownian motion</a>; <a href="/?q=ut%3AMarkov+chain">Markov chain</a>; <a href="/?q=ut%3Astability+in+distribution">stability in distribution</a>; <a href="/?q=ut%3Afeedback+control">feedback control</a>; <a href="/?q=ut%3Adiscrete-time+state+observation">discrete-time state observation</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 1485.93611" data-ciurl="/ci/07507277" data-biburl="/bibtex/07507277.bib" data-amsurl="/amsrefs/07507277.bib" data-xmlurl="/xml/07507277.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07507277.pdf" title="Zbl 1485.93611 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.2022.110210" aria-label="DOI for “Stabilisation in distribution of hybrid stochastic differential equations by feedback control based on discrete-time state observations”" title="10.1016/j.automatica.2022.110210">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://strathprints.strath.ac.uk/79172/1/Li_etal_Automatica_2022_Stabilization_in_distribution_of_hybrid_stochastic_differential_equations_by_feedback_control.pdf" 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, W. 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