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Article: Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach

TitlePolynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach
Authors
KeywordsLinear Matrix Inequality (Lmi)
Lyapunov Function
Polytopic System
Robust Stability
Time-Invariant Uncertainty
Issue Date2005
Citation
Ieee Transactions On Automatic Control, 2005, v. 50 n. 3, p. 365-370 How to Cite?
AbstractIn this note, robust stability of state-space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the homogeneous polynomially parameter-dependent quadratic Lyapunov functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists an HPD-QLF. The main result of the note is a sufficient condition for determining the sought HPD-QLF, which amounts to solving linear matrix inequalities (LMIs) derived via the complete square matricial representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach. © 2005 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/155259
ISSN
2015 Impact Factor: 2.777
2015 SCImago Journal Rankings: 4.238
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.accessioned2012-08-08T08:32:34Z-
dc.date.available2012-08-08T08:32:34Z-
dc.date.issued2005en_US
dc.identifier.citationIeee Transactions On Automatic Control, 2005, v. 50 n. 3, p. 365-370en_US
dc.identifier.issn0018-9286en_US
dc.identifier.urihttp://hdl.handle.net/10722/155259-
dc.description.abstractIn this note, robust stability of state-space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the homogeneous polynomially parameter-dependent quadratic Lyapunov functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists an HPD-QLF. The main result of the note is a sufficient condition for determining the sought HPD-QLF, which amounts to solving linear matrix inequalities (LMIs) derived via the complete square matricial representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach. © 2005 IEEE.en_US
dc.languageengen_US
dc.relation.ispartofIEEE Transactions on Automatic Controlen_US
dc.subjectLinear Matrix Inequality (Lmi)en_US
dc.subjectLyapunov Functionen_US
dc.subjectPolytopic Systemen_US
dc.subjectRobust Stabilityen_US
dc.subjectTime-Invariant Uncertaintyen_US
dc.titlePolynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approachen_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.doi10.1109/TAC.2005.843848en_US
dc.identifier.scopuseid_2-s2.0-16244419436en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-16244419436&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume50en_US
dc.identifier.issue3en_US
dc.identifier.spage365en_US
dc.identifier.epage370en_US
dc.identifier.isiWOS:000227747700007-
dc.publisher.placeUnited Statesen_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.citeulike201165-

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