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Conference Paper: On the admissible equilibrium points of nonlinear dynamical systems affected by parametric uncertainty: characterization via LMIs

TitleOn the admissible equilibrium points of nonlinear dynamical systems affected by parametric uncertainty: characterization via LMIs
Authors
KeywordsEquilibrium point
Infinite numbers
Linear matrix inequality problems
Numerical example
Parametric uncertainties
Issue Date2010
PublisherIEEE.
Citation
The 2010 IEEE International Symposium on Computer-Aided Control System Design (CACSD), Yokohama, Japan, 8-10 September 2010. in Proceedings of CACSD, 2010, p. 351-356 How to Cite?
AbstractThis paper investigates the set of admissible equilibrium points of nonlinear dynamical systems affected by parametric uncertainty. As it is well-known, determining this set is a difficult problem since one should compute the solutions of a system of nonlinear equations for all the admissible values of the uncertainty, which typically amounts to an infinite number of times. In order to address this problem, this paper proposes a characterization of this set via convex optimization for the case of polynomial nonlinearities and uncertainty constrained in a polytope. Specifically, it is shown that an upper bound of the smallest outer estimate with a freely selectable fixed shape can be obtained by solving a linear matrix inequality (LMI) problem built through the square matrix representation (SMR). Then, a necessary and sufficient condition is provided for establishing the tightness of the found upper bound. The proposed methodology and its benefits are illustrated through several numerical examples. © 2010 IEEE.
DescriptionProceedings of the IEEE International Symposium on Computer-Aided Control System Design, 2010, p. 351-356
Part of 2010 IEEE Multi-Conference on Systems and Control
Persistent Identifierhttp://hdl.handle.net/10722/135864
ISBN
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_HK
dc.date.accessioned2011-07-27T01:49:44Z-
dc.date.available2011-07-27T01:49:44Z-
dc.date.issued2010en_HK
dc.identifier.citationThe 2010 IEEE International Symposium on Computer-Aided Control System Design (CACSD), Yokohama, Japan, 8-10 September 2010. in Proceedings of CACSD, 2010, p. 351-356en_HK
dc.identifier.isbn978-1-4244-5355-9-
dc.identifier.urihttp://hdl.handle.net/10722/135864-
dc.descriptionProceedings of the IEEE International Symposium on Computer-Aided Control System Design, 2010, p. 351-356-
dc.descriptionPart of 2010 IEEE Multi-Conference on Systems and Control-
dc.description.abstractThis paper investigates the set of admissible equilibrium points of nonlinear dynamical systems affected by parametric uncertainty. As it is well-known, determining this set is a difficult problem since one should compute the solutions of a system of nonlinear equations for all the admissible values of the uncertainty, which typically amounts to an infinite number of times. In order to address this problem, this paper proposes a characterization of this set via convex optimization for the case of polynomial nonlinearities and uncertainty constrained in a polytope. Specifically, it is shown that an upper bound of the smallest outer estimate with a freely selectable fixed shape can be obtained by solving a linear matrix inequality (LMI) problem built through the square matrix representation (SMR). Then, a necessary and sufficient condition is provided for establishing the tightness of the found upper bound. The proposed methodology and its benefits are illustrated through several numerical examples. © 2010 IEEE.en_HK
dc.languageengen_US
dc.publisherIEEE.-
dc.relation.ispartofProceedings of the IEEE International Symposium on Computer-Aided Control System Designen_HK
dc.rightsProceedings of the IEEE International Symposium on Computer-Aided Control System Design. Copyright © IEEE.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rights©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.-
dc.subjectEquilibrium point-
dc.subjectInfinite numbers-
dc.subjectLinear matrix inequality problems-
dc.subjectNumerical example-
dc.subjectParametric uncertainties-
dc.titleOn the admissible equilibrium points of nonlinear dynamical systems affected by parametric uncertainty: characterization via LMIsen_HK
dc.typeConference_Paperen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=978-1-4244-5355-9&volume=&spage=351&epage=356&date=2010&atitle=On+the+admissible+equilibrium+points+of+nonlinear+dynamical+systems+affected+by+parametric+uncertainty:+characterization+via+LMIs-
dc.identifier.emailChesi, G:chesi@eee.hku.hken_HK
dc.identifier.authorityChesi, G=rp00100en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1109/CACSD.2010.5612860en_HK
dc.identifier.scopuseid_2-s2.0-78649897647en_HK
dc.identifier.hkuros187538en_US
dc.identifier.hkuros201441-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-78649897647&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.spage351en_HK
dc.identifier.epage356en_HK
dc.description.otherThe 2010 IEEE International Symposium on Computer-Aided Control System Design (CACSD), Yokohama, Japan, 8-10 September 2010. in Proceedings of CACSD, 2010, p. 351-356-
dc.identifier.scopusauthoridChesi, G=7006328614en_HK

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