Document Zbl 1250.93108

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Control Lett.</a> <a href="/?q=in%3A297619" title="Articles in this Issue">61, No. 3, 403-411 (2012)</a>. </div> <div class="abstract">Summary: The simultaneous semi-global $L_{p}$-stabilization and asymptotic stabilization in both semi-global and global cases are considered for continuous-time linear singular systems subject to input saturation. Based on the asymptotical property of the parametric generalized algebraic Riccati equations, a low-and-high gain state feedback control law and a scheduling technique are proposed. When applied to the singular system subject to input saturation and external disturbance, the semi-global finite-gain $L_{p}$-stabilization and semi-global/global asymptotic stabilization are obtained simultaneously. The obtained results reduce to the existing ones for non-singular linear systems when the linear singular system reduces to a non-singular system. Furthermore, our results also improve the semi-global stabilization results for singular systems with saturation in the absence of the external disturbance.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6082650">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%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%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%3A93B52" title="MSC2020">93B52</a> </td> <td class="space"> Feedback control </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asingular+systems">singular systems</a>; <a href="/?q=ut%3Ainput+saturation">input saturation</a>; <a href="/?q=ut%3Asemi-global+stabilization">semi-global stabilization</a>; <a href="/?q=ut%3Alow-and-high+gain+state+feedback">low-and-high gain state feedback</a>; <a href="/?q=ut%3ARiccati+equation">Riccati equation</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 1250.93108" data-ciurl="/ci/06082650" data-biburl="/bibtex/06082650.bib" data-amsurl="/amsrefs/06082650.bib" data-xmlurl="/xml/06082650.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06082650.pdf" title="Zbl 1250.93108 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.sysconle.2011.12.003" aria-label="DOI for “Simultaneous semi-global $L_p$-stabilization and asymptotical stabilization for singular systems subject to input saturation”" title="10.1016/j.sysconle.2011.12.003">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">Dai, L., Singular Control Systems (1989), Springer-Verlag: Springer-Verlag Berlin, Germany · <a href="/0669.93034" class="nowrap">Zbl 0669.93034</a></td> </tr><tr> <td>[2]</td> <td class="space">Xu, S. Y.; Lam, James, Robust Control and Filtering of Singular Systems (2006), Springer-Verlag: Springer-Verlag Berlin, Germany · <a href="/1114.93005" class="nowrap">Zbl 1114.93005</a></td> </tr><tr> <td>[3]</td> <td class="space">Lin, Z.; Saberi, A.; Teel, A. R., Simultaneous $L_p$-stabilization and internal stabilization of linear systems subject to input saturation-state feedback case, Systems & Control Letters, 25, 219-226 (1995) · <a href="/0877.93101" class="nowrap">Zbl 0877.93101</a></td> </tr><tr> <td>[4]</td> <td class="space">Lin, Z.; Saberi, A.; Teel, A. 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Y.; Terra, M. H., On the Lyapunov theorem for singular systems, IEEE Transactions on Automatic Control, 47, 1926-1930 (2002) · <a href="/1364.93570" class="nowrap">Zbl 1364.93570</a></td> </tr><tr> <td>[19]</td> <td class="space">A. Megretski, $ L_2$; A. Megretski, $ L_2$</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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