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Article: Convergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equations

TitleConvergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equations
Authors
KeywordsConvergence Rate
Discrete-Time
Gradient
Iteration
Lyapunov Equations
Markov Jump Linear Systems
Issue Date2008
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwa
Citation
Computers And Mathematics With Applications, 2008, v. 56 n. 12, p. 3070-3078 How to Cite?
AbstractThe solution of coupled discrete-time Markovian jump Lyapunov matrix equations (CDMJLMEs) is important in stability analysis and controller design for Markovian jump linear systems. This paper presents a simple and effective iterative method to produce numerical solutions to this class of matrix equations. The gradient-based algorithm is developed from an optimization point of view. A necessary and sufficient condition guaranteeing the convergence of the algorithm is established. This condition shows that the algorithm always converges provided the CDMJLMEs have unique solutions which is evidently different from the existing results that converge conditionally. A simple sufficient condition which is easy to test is also provided. The optimal step size in the algorithm such that the convergence rate of the algorithm is maximized is given explicitly. It turns out that an upper bound of the convergence rate is bounded by a function of the condition number of the augmented coefficient matrix of the CDMJLMEs. Some parameters are introduced to the algorithm that will potentially reduce the condition number and thus increase the convergence rate of the algorithm. A numerical example is used to illustrate the efficiency of the proposed approach. © 2008 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156986
ISSN
2015 Impact Factor: 1.398
2015 SCImago Journal Rankings: 1.092
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorZhou, Ben_US
dc.contributor.authorLam, Jen_US
dc.contributor.authorDuan, GRen_US
dc.date.accessioned2012-08-08T08:44:49Z-
dc.date.available2012-08-08T08:44:49Z-
dc.date.issued2008en_US
dc.identifier.citationComputers And Mathematics With Applications, 2008, v. 56 n. 12, p. 3070-3078en_US
dc.identifier.issn0898-1221en_US
dc.identifier.urihttp://hdl.handle.net/10722/156986-
dc.description.abstractThe solution of coupled discrete-time Markovian jump Lyapunov matrix equations (CDMJLMEs) is important in stability analysis and controller design for Markovian jump linear systems. This paper presents a simple and effective iterative method to produce numerical solutions to this class of matrix equations. The gradient-based algorithm is developed from an optimization point of view. A necessary and sufficient condition guaranteeing the convergence of the algorithm is established. This condition shows that the algorithm always converges provided the CDMJLMEs have unique solutions which is evidently different from the existing results that converge conditionally. A simple sufficient condition which is easy to test is also provided. The optimal step size in the algorithm such that the convergence rate of the algorithm is maximized is given explicitly. It turns out that an upper bound of the convergence rate is bounded by a function of the condition number of the augmented coefficient matrix of the CDMJLMEs. Some parameters are introduced to the algorithm that will potentially reduce the condition number and thus increase the convergence rate of the algorithm. A numerical example is used to illustrate the efficiency of the proposed approach. © 2008 Elsevier Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwaen_US
dc.relation.ispartofComputers and Mathematics with Applicationsen_US
dc.subjectConvergence Rateen_US
dc.subjectDiscrete-Timeen_US
dc.subjectGradienten_US
dc.subjectIterationen_US
dc.subjectLyapunov Equationsen_US
dc.subjectMarkov Jump Linear Systemsen_US
dc.titleConvergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equationsen_US
dc.typeArticleen_US
dc.identifier.emailLam, J:james.lam@hku.hken_US
dc.identifier.authorityLam, J=rp00133en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.camwa.2008.07.037en_US
dc.identifier.scopuseid_2-s2.0-55649083103en_US
dc.identifier.hkuros164192-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-55649083103&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume56en_US
dc.identifier.issue12en_US
dc.identifier.spage3070en_US
dc.identifier.epage3078en_US
dc.identifier.isiWOS:000261626600011-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridZhou, B=7401906664en_US
dc.identifier.scopusauthoridLam, J=7201973414en_US
dc.identifier.scopusauthoridDuan, GR=35229183800en_US

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