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Article: Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions

TitleRobust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions
Authors
KeywordsBounded variation rate uncertainty
LMI
Lyapunov function
Polytopic system
Robust stability
Issue Date2007
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica
Citation
Automatica, 2007, v. 43 n. 2, p. 309-316 How to Cite?
AbstractThis paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms. This class of Lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time-invariant perturbations. The main result of the paper is a sufficient condition to determine the sought Lyapunov function, which amounts to solving an LMI feasibility problem, derived via a suitable parameterization of polynomial homogeneous forms. Moreover, lower bounds on the maximum variation rate for which robust stability of the system is preserved, are shown to be computable in terms of generalized eigenvalue problems. Numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature. © 2006 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/73913
ISSN
2015 Impact Factor: 3.635
2015 SCImago Journal Rankings: 4.315
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_HK
dc.contributor.authorGarulli, Aen_HK
dc.contributor.authorTesi, Aen_HK
dc.contributor.authorVicino, Aen_HK
dc.date.accessioned2010-09-06T06:55:58Z-
dc.date.available2010-09-06T06:55:58Z-
dc.date.issued2007en_HK
dc.identifier.citationAutomatica, 2007, v. 43 n. 2, p. 309-316en_HK
dc.identifier.issn0005-1098en_HK
dc.identifier.urihttp://hdl.handle.net/10722/73913-
dc.description.abstractThis paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms. This class of Lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time-invariant perturbations. The main result of the paper is a sufficient condition to determine the sought Lyapunov function, which amounts to solving an LMI feasibility problem, derived via a suitable parameterization of polynomial homogeneous forms. Moreover, lower bounds on the maximum variation rate for which robust stability of the system is preserved, are shown to be computable in terms of generalized eigenvalue problems. Numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature. © 2006 Elsevier Ltd. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automaticaen_HK
dc.relation.ispartofAutomaticaen_HK
dc.subjectBounded variation rate uncertaintyen_HK
dc.subjectLMIen_HK
dc.subjectLyapunov functionen_HK
dc.subjectPolytopic systemen_HK
dc.subjectRobust stabilityen_HK
dc.titleRobust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functionsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0005-1098&volume=43&spage=309&epage=316&date=2007&atitle=Robust+stability+of+time-varying+polytopic+systems+via+parameter-dependent+homogeneous+Lyapunov+functionsen_HK
dc.identifier.emailChesi, G:chesi@eee.hku.hken_HK
dc.identifier.authorityChesi, G=rp00100en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.automatica.2006.08.024en_HK
dc.identifier.scopuseid_2-s2.0-33845934993en_HK
dc.identifier.hkuros130703en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33845934993&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume43en_HK
dc.identifier.issue2en_HK
dc.identifier.spage309en_HK
dc.identifier.epage316en_HK
dc.identifier.isiWOS:000243670600011-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridChesi, G=7006328614en_HK
dc.identifier.scopusauthoridGarulli, A=7003697493en_HK
dc.identifier.scopusauthoridTesi, A=7007124648en_HK
dc.identifier.scopusauthoridVicino, A=7006250298en_HK

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