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Article: Homogeneous Lyapunov functions for systems with structured uncertainties

TitleHomogeneous Lyapunov functions for systems with structured uncertainties
Authors
KeywordsHomogeneous Forms
Linear Matrix Inequalities (Lmi)
Lyapunov Function
Robustness
Issue Date2003
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica
Citation
Automatica, 2003, v. 39 n. 6, p. 1027-1035 How to Cite?
AbstractThe problem addressed in this paper is the construction of homogeneous polynomial Lyapunov functions (HPLFs) for linear systems with time-varying structured uncertainties. A sufficient condition for the existence of an HPLF of given degree is formulated in terms of a linear matrix inequalities (LMI) feasibility problem. This condition turns out to be also necessary in some cases depending on the dimension of the system and the degree of the Lyapunov function. The maximum ℓ∞ norm of the parametric uncertainty for which there exists a homogeneous polynomial Lyapunov function is computed by solving a generalized eigenvalue problem. The construction of such Lyapunov functions is efficiently performed by means of popular convex optimization tools for the solution of problems in LMI form. Comparisons with other classes of Lyapunov functions through numerical examples taken from the literature show that HPLFs are a powerful tool for robustness analysis. © 2003 Published by Elsevier Science Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/155203
ISSN
2015 Impact Factor: 3.635
2015 SCImago Journal Rankings: 4.315
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.contributor.authorGarulli, Aen_US
dc.contributor.authorTesi, Aen_US
dc.contributor.authorVicino, Aen_US
dc.date.accessioned2012-08-08T08:32:19Z-
dc.date.available2012-08-08T08:32:19Z-
dc.date.issued2003en_US
dc.identifier.citationAutomatica, 2003, v. 39 n. 6, p. 1027-1035en_US
dc.identifier.issn0005-1098en_US
dc.identifier.urihttp://hdl.handle.net/10722/155203-
dc.description.abstractThe problem addressed in this paper is the construction of homogeneous polynomial Lyapunov functions (HPLFs) for linear systems with time-varying structured uncertainties. A sufficient condition for the existence of an HPLF of given degree is formulated in terms of a linear matrix inequalities (LMI) feasibility problem. This condition turns out to be also necessary in some cases depending on the dimension of the system and the degree of the Lyapunov function. The maximum ℓ∞ norm of the parametric uncertainty for which there exists a homogeneous polynomial Lyapunov function is computed by solving a generalized eigenvalue problem. The construction of such Lyapunov functions is efficiently performed by means of popular convex optimization tools for the solution of problems in LMI form. Comparisons with other classes of Lyapunov functions through numerical examples taken from the literature show that HPLFs are a powerful tool for robustness analysis. © 2003 Published by Elsevier Science Ltd.en_US
dc.languageengen_US
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automaticaen_US
dc.relation.ispartofAutomaticaen_US
dc.subjectHomogeneous Formsen_US
dc.subjectLinear Matrix Inequalities (Lmi)en_US
dc.subjectLyapunov Functionen_US
dc.subjectRobustnessen_US
dc.titleHomogeneous Lyapunov functions for systems with structured uncertaintiesen_US
dc.typeArticleen_US
dc.identifier.emailChesi, G:chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/S0005-1098(03)00039-6en_US
dc.identifier.scopuseid_2-s2.0-0038372478en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0038372478&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume39en_US
dc.identifier.issue6en_US
dc.identifier.spage1027en_US
dc.identifier.epage1035en_US
dc.identifier.isiWOS:000182900900009-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridChesi, G=7006328614en_US
dc.identifier.scopusauthoridGarulli, A=7003697493en_US
dc.identifier.scopusauthoridTesi, A=7007124648en_US
dc.identifier.scopusauthoridVicino, A=7006250298en_US
dc.identifier.citeulike7680517-

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