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Conference Paper: On the estimation and control of the domain of attraction through rational Lyapunov functions

TitleOn the estimation and control of the domain of attraction through rational Lyapunov functions
Authors
KeywordsContinuous time nonlinear systems
Control problems
Domain of attraction
Equilibrium point
Estimation problem
Issue Date2012
PublisherAmerican Automatic Control Council. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000030
Citation
The 2012 American Control Conference (ACC 2012), Montréal, Canada, 27-29 June 2012. In American Control Conference Proceedings, 2012, p. 3322-3327 How to Cite?
AbstractThis paper addresses the estimation and control of the domain of attraction (DA) of equilibrium points through rational Lyapunov functions (LFs). Specifically, continuous-time nonlinear systems with polynomial nonlinearities are considered. The estimation problem consists of computing the largest estimate of the DA (LEDA) provided by a given rational LF. The control problem consists of computing a polynomial static output controller of given degree for maximizing such a LEDA. It is shown that lower bounds of the LEDA in the estimation problem, or the maximum achievable LEDA in the control problem, can be obtained by solving either an eigenvalue problem or a generalized eigenvalue problem with smaller dimension. The conservatism of these lower bounds can be reduced by increasing the degree of some multipliers introduced in the construction of the optimization problems. Moreover, a necessary and sufficient condition for establishing tightness of the found lower bounds is provided. Some numerical examples illustrate the use of the proposed results. © 2012 AACC American Automatic Control Council).
Persistent Identifierhttp://hdl.handle.net/10722/153079
ISBN
ISSN

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.date.accessioned2012-07-16T09:55:45Z-
dc.date.available2012-07-16T09:55:45Z-
dc.date.issued2012en_US
dc.identifier.citationThe 2012 American Control Conference (ACC 2012), Montréal, Canada, 27-29 June 2012. In American Control Conference Proceedings, 2012, p. 3322-3327en_US
dc.identifier.isbn978-1-4577-1096-4-
dc.identifier.issn0743-1619-
dc.identifier.urihttp://hdl.handle.net/10722/153079-
dc.description.abstractThis paper addresses the estimation and control of the domain of attraction (DA) of equilibrium points through rational Lyapunov functions (LFs). Specifically, continuous-time nonlinear systems with polynomial nonlinearities are considered. The estimation problem consists of computing the largest estimate of the DA (LEDA) provided by a given rational LF. The control problem consists of computing a polynomial static output controller of given degree for maximizing such a LEDA. It is shown that lower bounds of the LEDA in the estimation problem, or the maximum achievable LEDA in the control problem, can be obtained by solving either an eigenvalue problem or a generalized eigenvalue problem with smaller dimension. The conservatism of these lower bounds can be reduced by increasing the degree of some multipliers introduced in the construction of the optimization problems. Moreover, a necessary and sufficient condition for establishing tightness of the found lower bounds is provided. Some numerical examples illustrate the use of the proposed results. © 2012 AACC American Automatic Control Council).-
dc.languageengen_US
dc.publisherAmerican Automatic Control Council. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000030-
dc.relation.ispartofAmerican Control Conference Proceedingsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectContinuous time nonlinear systems-
dc.subjectControl problems-
dc.subjectDomain of attraction-
dc.subjectEquilibrium point-
dc.subjectEstimation problem-
dc.titleOn the estimation and control of the domain of attraction through rational Lyapunov functionsen_US
dc.typeConference_Paperen_US
dc.identifier.emailChesi, G: chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturepublished_or_final_version-
dc.identifier.scopuseid_2-s2.0-84869387681-
dc.identifier.hkuros201445en_US
dc.identifier.spage3322en_US
dc.identifier.epage3327en_US
dc.publisher.placeUnited States-
dc.customcontrol.immutablesml 140122-

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