Cascaded-based stabilization of time-varying systems using second-order sliding modes
Identifieur interne : 001402 ( Hal/Curation ); précédent : 001401; suivant : 001403Cascaded-based stabilization of time-varying systems using second-order sliding modes
Auteurs : Antonio Estrada [France] ; Antonio Loria [France] ; Raul Santiesteban [France] ; Leonid Fridman [Mexique]Source :
Abstract
We present a result on stabilization of strict feedback systems with unknown disturbances based on the so-called twisting algorithm, a second-order sliding mode controller for the double integrator. The novelty of the note relies in the stability analysis of the closed-loop system and the relaxation of stability conditions (we do not assume boundedness of trajectories). The proof of the main result is constructed along similar lines as for well-established theorems for nonlinear time-varying systems in cascade, with continuous right-hand sides. Although we restrict our analysis to second-order systems, the purpose of this note is to settle the basis for a methodological stability analysis approach for higher-order systems in strict feedback form, under the influence of uncertain perturbations. An illustrative example is provided.
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DOI: 10.1093/imamci/dns018
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An illustrative example is provided.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Cascaded-based stabilization of time-varying systems using second-order sliding modes</title><author role="aut"><persName><forename type="first">Antonio</forename><surname>Estrada</surname></persName><email></email><idno type="halauthor">529684</idno><affiliation ref="#struct-189952"></affiliation></author><author role="aut"><persName><forename type="first">Antonio</forename><surname>Loria</surname></persName><email>loria@lss.supelec.fr</email><ptr type="url" target="http://www.lss.supelec.fr/perso/loria_antonio/"></ptr><idno type="halauthor">858111</idno><affiliation ref="#struct-1289"></affiliation></author><author role="aut"><persName><forename type="first">Raul</forename><surname>Santiesteban</surname></persName><email></email><idno type="halauthor">714484</idno><affiliation ref="#struct-189952"></affiliation></author><author role="aut"><persName><forename type="first">Leonid</forename><surname>Fridman</surname></persName><email></email><idno type="halauthor">254718</idno><affiliation ref="#struct-155865"></affiliation></author><editor role="depositor"><persName><forename>Antonio</forename><surname>Loria</surname></persName><email>loria@lss.supelec.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2013-06-07 09:42:53</date><date type="whenModified">2016-03-22 01:25:39</date><date type="whenReleased">2013-06-07 10:43:56</date><date type="whenProduced">2013</date><date type="whenEndEmbargoed">2013-06-07</date><ref type="file" target="https://hal.archives-ouvertes.fr/hal-00831445/document"><date notBefore="2013-06-07"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.archives-ouvertes.fr/hal-00831445/file/vfinal_IMA_JMCICascades.pdf"><date notBefore="2013-06-07"></date></ref></edition><respStmt><resp>contributor</resp><name key="147168"><persName><forename>Antonio</forename><surname>Loria</surname></persName><email>loria@lss.supelec.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-00831445</idno><idno type="halUri">https://hal.archives-ouvertes.fr/hal-00831445</idno><idno type="halBibtex">estrada:hal-00831445</idno><idno type="halRefHtml">IMA J Mathematical Control Information, 2013, 30 (1), pp.115-128. <10.1093/imamci/dns018></idno><idno type="halRef">IMA J Mathematical Control Information, 2013, 30 (1), pp.115-128. <10.1093/imamci/dns018></idno></publicationStmt><seriesStmt><idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno><idno type="stamp" n="L2S">Laboratoire des signaux et systèmes</idno><idno type="stamp" n="SUPELEC">SUPELEC</idno><idno type="stamp" n="SUP_LSS" p="CENTRALESUPELEC">Laboratoire des Signaux et Systèmes</idno><idno type="stamp" n="SUP_SYSTEMES" p="CENTRALESUPELEC">Pôle Systèmes</idno><idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="CENTRALESUPELEC">Ecole CentraleSupélec</idno></seriesStmt><notesStmt><note type="audience" n="2">International</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Cascaded-based stabilization of time-varying systems using second-order sliding modes</title><author role="aut"><persName><forename type="first">Antonio</forename><surname>Estrada</surname></persName><idno type="halAuthorId">529684</idno><affiliation ref="#struct-189952"></affiliation></author><author role="aut"><persName><forename type="first">Antonio</forename><surname>Loria</surname></persName><email>loria@lss.supelec.fr</email><ptr type="url" target="http://www.lss.supelec.fr/perso/loria_antonio/"></ptr><idno type="halAuthorId">858111</idno><affiliation ref="#struct-1289"></affiliation></author><author role="aut"><persName><forename type="first">Raul</forename><surname>Santiesteban</surname></persName><idno type="halAuthorId">714484</idno><affiliation ref="#struct-189952"></affiliation></author><author role="aut"><persName><forename type="first">Leonid</forename><surname>Fridman</surname></persName><idno type="halAuthorId">254718</idno><affiliation ref="#struct-155865"></affiliation></author></analytic><monogr><idno type="halJournalId" status="INCOMING">83289</idno><title level="j">IMA J Mathematical Control Information</title><imprint><biblScope unit="volume">30</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="pp">115-128</biblScope><date type="datePub">2013</date></imprint></monogr><idno type="doi">10.1093/imamci/dns018</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><classCode scheme="halDomain" n="info.info-au">Computer Science [cs]/Automatic Control Engineering</classCode><classCode scheme="halDomain" n="math.math-ds">Mathematics [math]/Dynamical Systems [math.DS]</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><abstract xml:lang="en">We present a result on stabilization of strict feedback systems with unknown disturbances based on the so-called twisting algorithm, a second-order sliding mode controller for the double integrator. The novelty of the note relies in the stability analysis of the closed-loop system and the relaxation of stability conditions (we do not assume boundedness of trajectories). The proof of the main result is constructed along similar lines as for well-established theorems for nonlinear time-varying systems in cascade, with continuous right-hand sides. Although we restrict our analysis to second-order systems, the purpose of this note is to settle the basis for a methodological stability analysis approach for higher-order systems in strict feedback form, under the influence of uncertain perturbations. An illustrative example is provided.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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