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Article: LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems

TitleLMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems
Authors
KeywordsDomain Of Attraction
Homogeneous Forms
Linear Matrix Inequalities
Lyapunov Functions
Issue Date2005
PublisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/5510
Citation
International Journal Of Robust And Nonlinear Control, 2005, v. 15 n. 1, p. 35-49 How to Cite?
AbstractThe problem of estimating the domain of attraction (DA) of equilibria is considered for odd polynomial systems. Specifically, the computation of the optimal quadratic Lyapunov function (OQLF), i.e. the quadratic Lyapunov function (QLF) which maximizes the volume of the largest estimate of the DA (LEDA), is addressed. In order to tackle this double non-convex optimization problem, a relaxation approach based on homogeneous polynomial forms is proposed. The first contribution of the paper shows that a lower bound of the LEDA for a fixed QLF can be obtained via linear matrix inequalities (LMIs) based procedures. Also, condition for checking tightness of the lower bound are provided. The second contribution is a strategy for selecting a good starting point for the OQLF search, which is based on the volume maximization of the region where the time derivative of the QLFs is negative and is given in terms of LMIs. Several application examples are presented to illustrate the numerical behaviour of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/155245
ISSN
2015 Impact Factor: 2.527
2015 SCImago Journal Rankings: 2.134
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.accessioned2012-08-08T08:32:31Z-
dc.date.available2012-08-08T08:32:31Z-
dc.date.issued2005en_US
dc.identifier.citationInternational Journal Of Robust And Nonlinear Control, 2005, v. 15 n. 1, p. 35-49en_US
dc.identifier.issn1049-8923en_US
dc.identifier.urihttp://hdl.handle.net/10722/155245-
dc.description.abstractThe problem of estimating the domain of attraction (DA) of equilibria is considered for odd polynomial systems. Specifically, the computation of the optimal quadratic Lyapunov function (OQLF), i.e. the quadratic Lyapunov function (QLF) which maximizes the volume of the largest estimate of the DA (LEDA), is addressed. In order to tackle this double non-convex optimization problem, a relaxation approach based on homogeneous polynomial forms is proposed. The first contribution of the paper shows that a lower bound of the LEDA for a fixed QLF can be obtained via linear matrix inequalities (LMIs) based procedures. Also, condition for checking tightness of the lower bound are provided. The second contribution is a strategy for selecting a good starting point for the OQLF search, which is based on the volume maximization of the region where the time derivative of the QLFs is negative and is given in terms of LMIs. Several application examples are presented to illustrate the numerical behaviour of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.en_US
dc.languageengen_US
dc.publisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/5510en_US
dc.relation.ispartofInternational Journal of Robust and Nonlinear Controlen_US
dc.subjectDomain Of Attractionen_US
dc.subjectHomogeneous Formsen_US
dc.subjectLinear Matrix Inequalitiesen_US
dc.subjectLyapunov Functionsen_US
dc.titleLMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systemsen_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.doi10.1002/rnc.967en_US
dc.identifier.scopuseid_2-s2.0-10844286528en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-10844286528&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume15en_US
dc.identifier.issue1en_US
dc.identifier.spage35en_US
dc.identifier.epage49en_US
dc.identifier.isiWOS:000226060700004-
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

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