Document Zbl 1329.93149

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In this paper, a fundamental stabilization problem is investigated for a class of sampled-data systems under noisy sampling interval. The stochastic sampled-data control system under consideration is first converted into a discrete-time system whose system matrix is represented as an equivalent yet tractable form via the matrix exponential computation. Then, by introducing a Vandermonde matrix, the mathematical expectation of the quadratic form of the system matrix is computed. By recurring to the Kronecker product operation, a sampled-data stabilization controller is designed such that the closed-loop system is stochastically stable in the presence of noisy sampling interval. Subsequently, a special case is considered where the sampling interval obeys the continuous uniform distribution and the corresponding stabilization controller is designed. Finally, a numerical simulation example is provided to demonstrate the effectiveness of the proposed design approach.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6524060">Cited in <strong>27</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%3A93C57" title="MSC2020">93C57</a> </td> <td class="space"> Sampled-data control/observation systems </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%3A93B50" title="MSC2020">93B50</a> </td> <td class="space"> Synthesis problems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amatrix+exponential">matrix exponential</a>; <a href="/?q=ut%3Anoisy+sampling+interval">noisy sampling interval</a>; <a href="/?q=ut%3Asampled-data+control+systems">sampled-data control systems</a>; <a href="/?q=ut%3Astochastic+control">stochastic control</a>; <a href="/?q=ut%3Asynthesis+of+stochastic+systems">synthesis of stochastic systems</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 1329.93149" data-ciurl="/ci/06524060" data-biburl="/bibtex/06524060.bib" data-amsurl="/amsrefs/06524060.bib" data-xmlurl="/xml/06524060.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06524060.pdf" title="Zbl 1329.93149 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.2015.10.005" aria-label="DOI for “Stabilization for sampled-data systems under noisy sampling interval”" title="10.1016/j.automatica.2015.10.005">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://bura.brunel.ac.uk/handle/2438/11791" 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">Alexandre, S., A novel stability analysis of linear systems under asynchronous samplings, Automatica, 48, 1, 177-182 (2012) · <a href="/1244.93095" class="nowrap">Zbl 1244.93095</a></td> </tr><tr> <td>[3]</td> <td class="space">Ding, D.; Wang, Z.; Lam, J.; Shen, B., Finite-horizon $H_\infty$ control for discrete time-varying systems with randomly occurring nonlinearities and fading measurements, IEEE Transactions on Automatic Control, 60, 9, 2488-2493 (2015) · <a href="/1360.93646" class="nowrap">Zbl 1360.93646</a></td> </tr><tr> <td>[4]</td> <td class="space">Ding, D.; Wang, Z.; Shen, B.; Dong, H., Envelope-constrained $H_\infty$ filtering with fading measurements and randomly occurring nonlinearities: the finite horizon case, Automatica, 55, 37-45 (2015) · <a href="/1378.93125" class="nowrap">Zbl 1378.93125</a></td> </tr><tr> <td>[5]</td> <td class="space">Dong, H.; Wang, Z.; Gao, H., Distributed $H_\infty$ filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks, IEEE Transactions on Industrial Electronics, 60, 10, 4665-4672 (2013)</td> </tr><tr> <td>[6]</td> <td class="space">Fridman, E.; Seuret, A.; Richard, J. P., Robust sampled-data stabilization of linear systems: an input delay approach, Automatica, 40, 8, 1441-1446 (2004) · <a href="/1072.93018" class="nowrap">Zbl 1072.93018</a></td> </tr><tr> <td>[7]</td> <td class="space">Gao, H.; Wu, J.; Shi, P., Robust sampled-data $H_\infty$ control with stochastic sampling, Automatica, 45, 7, 1729-1736 (2009) · <a href="/1184.93039" class="nowrap">Zbl 1184.93039</a></td> </tr><tr> <td>[9]</td> <td class="space">Lam, H. K., Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach, IEEE Transactions on Systems, Man and Cybernetics, Part B-Cybernetics, 42, 1, 258-267 (2012)</td> </tr><tr> <td>[10]</td> <td class="space">Moler, C.; Van Loan, C., Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Review, 45, 1, 3-49 (2003) · <a href="/1030.65029" class="nowrap">Zbl 1030.65029</a></td> </tr><tr> <td>[11]</td> <td class="space">Oishi, Y.; Fujioka, H., Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities, Automatica, 46, 8, 1327-1333 (2010) · <a href="/1205.93100" class="nowrap">Zbl 1205.93100</a></td> </tr><tr> <td>[12]</td> <td class="space">Shen, B., A survey on the applications of the Krein-space theory in signal estimation, Systems Science & Control Engineering: An Open Access Journal, 2, 1, 143-149 (2014)</td> </tr><tr> <td>[13]</td> <td class="space">Suplin, V.; Fridman, E.; Shaked, U., Sampled-data $H_\infty$ control and filtering: Nonuniform uncertain sampling, Automatica, 43, 6, 1072-1083 (2007) · <a href="/1282.93171" class="nowrap">Zbl 1282.93171</a></td> </tr><tr> <td>[14]</td> <td class="space">Van Loan, C. F., Computing integrals involving the matrix exponential, IEEE Transactions on Automatic Control, AC-23, 3, 395-404 (1978) · <a href="/0387.65013" class="nowrap">Zbl 0387.65013</a></td> </tr><tr> <td>[15]</td> <td class="space">Wei, G.; Liu, S.; Song, Y.; Liu, Y., Probability-guaranteed set-membership filtering for systems with incomplete measurements, Automatica, 60, 12-16 (2015) · <a href="/1331.93205" class="nowrap">Zbl 1331.93205</a></td> </tr><tr> <td>[16]</td> <td class="space">Xu, Y.; Su, H.; Pan, Y., Output feedback stabilization for Markov-based nonuniformly sampled-data networked control systems, Systems & Control Letters, 62, 8, 656-663 (2013) · <a href="/1279.93087" class="nowrap">Zbl 1279.93087</a></td> </tr><tr> <td>[17]</td> <td class="space">Young, S. S., Stability and stabilization of nonuniform sampling systems, Automatica, 44, 12, 3222-3226 (2008) · <a href="/1153.93450" class="nowrap">Zbl 1153.93450</a></td> </tr><tr> <td>[18]</td> <td class="space">Zhang, W.; Yu, L., Stabilization of sampled-data control systems with control inputs missing, IEEE Transactions on Automatic Control, 55, 2, 447-452 (2010) · <a href="/1368.93586" class="nowrap">Zbl 1368.93586</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. 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. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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