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Article: A nonconservative LMI condition for stability of switched systems with guaranteed dwell time

TitleA nonconservative LMI condition for stability of switched systems with guaranteed dwell time
Authors
KeywordsDwell Time
Homogeneous Polynomial
Lmi
Lypaunov Function
Switched System
Issue Date2012
Citation
Ieee Transactions On Automatic Control, 2012, v. 57 n. 5, p. 1297-1302 How to Cite?
AbstractEnsuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems. Several methods have been proposed in the literature to address this problem, but unfortunately they provide sufficient conditions only. This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials. Several properties are proved for this condition, in particular that it is also necessary for a sufficiently large degree of these functions. As a result, the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well. Some examples illustrate the proposed approach. © 2012 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/155754
ISSN
2015 Impact Factor: 2.777
2015 SCImago Journal Rankings: 4.238
ISI Accession Number ID
Funding AgencyGrant Number
University of Hong Kong201010159010
Science Foundation of Ireland07/IN.1/I1838
07/IN.1/I901
Conselho Nacional de Desenvolvimento Cientifico e Tecnologicomdash;CNPq, Brazil
Funding Information:

Manuscript received December 26, 2010; revised May 23, 2011; accepted September 28, 2011. Date of publication November 02, 2011; date of current version April 19, 2012. This work was supported in part by the University of Hong Kong (under Research Grant 201010159010), the Science Foundation of Ireland (under Research Grants 07/IN.1/I1838 and 07/IN.1/I901) and the Conselho Nacional de Desenvolvimento Cientifico e Tecnologicomdash;CNPq, Brazil. Recommended by Associate Editor J. Daafouz.

References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.contributor.authorColaneri, Pen_US
dc.contributor.authorGeromel, JCen_US
dc.contributor.authorMiddleton, Ren_US
dc.contributor.authorShorten, Ren_US
dc.date.accessioned2012-08-08T08:35:11Z-
dc.date.available2012-08-08T08:35:11Z-
dc.date.issued2012en_US
dc.identifier.citationIeee Transactions On Automatic Control, 2012, v. 57 n. 5, p. 1297-1302en_US
dc.identifier.issn0018-9286en_US
dc.identifier.urihttp://hdl.handle.net/10722/155754-
dc.description.abstractEnsuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems. Several methods have been proposed in the literature to address this problem, but unfortunately they provide sufficient conditions only. This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials. Several properties are proved for this condition, in particular that it is also necessary for a sufficiently large degree of these functions. As a result, the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well. Some examples illustrate the proposed approach. © 2012 IEEE.en_US
dc.languageengen_US
dc.relation.ispartofIEEE Transactions on Automatic Controlen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectDwell Timeen_US
dc.subjectHomogeneous Polynomialen_US
dc.subjectLmien_US
dc.subjectLypaunov Functionen_US
dc.subjectSwitched Systemen_US
dc.titleA nonconservative LMI condition for stability of switched systems with guaranteed dwell timeen_US
dc.typeArticleen_US
dc.identifier.emailChesi, G:chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1109/TAC.2011.2174665en_US
dc.identifier.scopuseid_2-s2.0-84860489735en_US
dc.identifier.hkuros201428-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84860489735&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume57en_US
dc.identifier.issue5en_US
dc.identifier.spage1297en_US
dc.identifier.epage1302en_US
dc.identifier.isiWOS:000303325100023-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridChesi, G=7006328614en_US
dc.identifier.scopusauthoridColaneri, P=7004151032en_US
dc.identifier.scopusauthoridGeromel, JC=7005668079en_US
dc.identifier.scopusauthoridMiddleton, R=7203034709en_US
dc.identifier.scopusauthoridShorten, R=7003386909en_US
dc.identifier.citeulike10625293-

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