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Article: Lyapunov stability of abstract nonlinear dynamic system in Banach space

TitleLyapunov stability of abstract nonlinear dynamic system in Banach space
Authors
Xu, GQYung, SP
KeywordsAbstract nonlinear dynamic equation
Banach space
Lyapunov stability
Issue Date2003
PublisherOxford University Press. The Journal's web site is located at http://imamci.oxfordjournals.org/
Citation
Ima Journal Of Mathematical Control And Information, 2003, v. 20 n. 1, p. 105-127 How to Cite?
DOI: http://dx.doi.org/10.1093/imamci/20.1.105
AbstractThe Lyapunov stability theory for nonlinear time-varying dynamic system in Banach space is given in this paper. The Lyapunov stable theorem and the Barbashin-Krasovskii-LaSalle invariant set principle in classical theory are extended to infinite-dimensional Banach space. Under the assumptions of the existence of solution and the additive property of motions, sufficient and necessary conditions for uniform stability and uniform asymptotic stability are obtained, and the Lyapunov functions are explicitly constructed. This extension can be used as a criterion of stability for continuous and discontinuous systems.
Persistent Identifierhttp://hdl.handle.net/10722/48607
ISSN
0265-0754
2023 Impact Factor: 1.6
2023 SCImago Journal Rankings: 0.483
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorXu, GQen_HK
dc.contributor.authorYung, SPen_HK
dc.date.accessioned2008-05-22T04:18:49Z-
dc.date.available2008-05-22T04:18:49Z-
dc.date.issued2003en_HK
dc.identifier.citationIma Journal Of Mathematical Control And Information, 2003, v. 20 n. 1, p. 105-127en_HK
dc.identifier.issn0265-0754en_HK
dc.identifier.urihttp://hdl.handle.net/10722/48607-
dc.description.abstractThe Lyapunov stability theory for nonlinear time-varying dynamic system in Banach space is given in this paper. The Lyapunov stable theorem and the Barbashin-Krasovskii-LaSalle invariant set principle in classical theory are extended to infinite-dimensional Banach space. Under the assumptions of the existence of solution and the additive property of motions, sufficient and necessary conditions for uniform stability and uniform asymptotic stability are obtained, and the Lyapunov functions are explicitly constructed. This extension can be used as a criterion of stability for continuous and discontinuous systems.en_HK
dc.format.extent252738 bytes-
dc.format.extent3630 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherOxford University Press. The Journal's web site is located at http://imamci.oxfordjournals.org/en_HK
dc.relation.ispartofIMA Journal of Mathematical Control and Informationen_HK
dc.subjectAbstract nonlinear dynamic equationen_HK
dc.subjectBanach spaceen_HK
dc.subjectLyapunov stabilityen_HK
dc.titleLyapunov stability of abstract nonlinear dynamic system in Banach spaceen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0265-0754&volume=20&issue=1&spage=105&epage=127&date=2003&atitle=Lyapunov+stability+of+abstract+nonlinear++dynamic+system++in+Banach+spaceen_HK
dc.identifier.emailYung, SP:spyung@hkucc.hku.hken_HK
dc.identifier.authorityYung, SP=rp00838en_HK
dc.description.naturepostprinten_HK
dc.identifier.doi10.1093/imamci/20.1.105en_HK
dc.identifier.scopuseid_2-s2.0-0037335367en_HK
dc.identifier.hkuros76457-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0037335367&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume20en_HK
dc.identifier.issue1en_HK
dc.identifier.spage105en_HK
dc.identifier.epage127en_HK
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridXu, GQ=7404263948en_HK
dc.identifier.scopusauthoridYung, SP=7006540951en_HK
dc.identifier.issnl0265-0754-

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