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Article: Estimating the domain of attraction for non-polynomial systems via LMI optimizations

TitleEstimating the domain of attraction for non-polynomial systems via LMI optimizations
Authors
KeywordsDomain of attraction
Equilibrium point
LMI
Lyapunov function
Nonlinear system
Issue Date2009
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica
Citation
Automatica, 2009, v. 45 n. 6, p. 1536-1541 How to Cite?
AbstractThis paper proposes a strategy for estimating the domain of attraction (DA) for non-polynomial systems via Lyapunov functions (LFs). The idea consists of converting the non-polynomial optimization arising for a chosen LF in a polynomial one, which can be solved via LMI optimizations. This is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polytope which allows us to take into account the worst-case remainders in truncated Taylor expansions. Moreover, a condition is provided for ensuring asymptotical convergence to the largest estimate achievable with the chosen LF, and another condition is provided for establishing whether such an estimate has been found. The proposed strategy can readily be exploited with variable LFs in order to search for optimal estimates. Lastly, it is worth remarking that no other method is available to estimate the DA for non-polynomial systems via LMIs. © 2009 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/58821
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.date.accessioned2010-05-31T03:37:30Z-
dc.date.available2010-05-31T03:37:30Z-
dc.date.issued2009en_HK
dc.identifier.citationAutomatica, 2009, v. 45 n. 6, p. 1536-1541en_HK
dc.identifier.issn0005-1098en_HK
dc.identifier.urihttp://hdl.handle.net/10722/58821-
dc.description.abstractThis paper proposes a strategy for estimating the domain of attraction (DA) for non-polynomial systems via Lyapunov functions (LFs). The idea consists of converting the non-polynomial optimization arising for a chosen LF in a polynomial one, which can be solved via LMI optimizations. This is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polytope which allows us to take into account the worst-case remainders in truncated Taylor expansions. Moreover, a condition is provided for ensuring asymptotical convergence to the largest estimate achievable with the chosen LF, and another condition is provided for establishing whether such an estimate has been found. The proposed strategy can readily be exploited with variable LFs in order to search for optimal estimates. Lastly, it is worth remarking that no other method is available to estimate the DA for non-polynomial systems via LMIs. © 2009 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.subjectDomain of attractionen_HK
dc.subjectEquilibrium pointen_HK
dc.subjectLMIen_HK
dc.subjectLyapunov functionen_HK
dc.subjectNonlinear systemen_HK
dc.titleEstimating the domain of attraction for non-polynomial systems via LMI optimizationsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0005-1098&volume=45&spage=1536&epage=1541&date=2009&atitle=Estimating+the+domain+of+attraction+for+non-polynomial+systems+via+LMI+optimizationsen_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.2009.02.011en_HK
dc.identifier.scopuseid_2-s2.0-67349196818en_HK
dc.identifier.hkuros156194en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-67349196818&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume45en_HK
dc.identifier.issue6en_HK
dc.identifier.spage1536en_HK
dc.identifier.epage1541en_HK
dc.identifier.eissn1873-2836-
dc.identifier.isiWOS:000267199500025-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridChesi, G=7006328614en_HK

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