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Conference Paper: Measuring the instability in continuous-time linear systems with polytopic uncertainty

TitleMeasuring the instability in continuous-time linear systems with polytopic uncertainty
Authors
Issue Date2013
PublisherInstitute of Electrical and Electronics Engineers. The Journal's web site is located at http://www.ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000188
Citation
The 52nd IEEE Conference on Decision and Control (CDC 2013), Florence, Italy, 10-13 December 2013. In IEEE Conference on Decision and Control Proceedings, 2013, p. 1131-1136 How to Cite?
AbstractMeasuring the instability of dynamical systems is an important problem for control synthesis. This paper considers continuous-time linear systems affected by structured uncertainty, and addresses the computation of the robust instability measure defined as the largest sum of the real parts of the unstable eigenvalues over all admissible uncertainties. In particular, it is supposed that the coefficients of the system are affine linear functions of an uncertain vector constrained into a polytope. First, an equivalent reformulation of this robust instability measure into a suitable robust stability margin of a finite family of systems is proposed. Second, a linear matrix inequality (LMI) condition is provided to establish upper bounds of the robust instability measure through the use of homogeneous Lyapunov functions. Third, a sufficient and necessary condition for establishing the optimality of a computed upper bound is proposed. Some numerical examples illustrate the proposed results. © 2013 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/199364
ISBN
ISSN

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.date.accessioned2014-07-22T01:15:37Z-
dc.date.available2014-07-22T01:15:37Z-
dc.date.issued2013en_US
dc.identifier.citationThe 52nd IEEE Conference on Decision and Control (CDC 2013), Florence, Italy, 10-13 December 2013. In IEEE Conference on Decision and Control Proceedings, 2013, p. 1131-1136en_US
dc.identifier.isbn978-1-4673-5717-3-
dc.identifier.issn0743-1546-
dc.identifier.urihttp://hdl.handle.net/10722/199364-
dc.description.abstractMeasuring the instability of dynamical systems is an important problem for control synthesis. This paper considers continuous-time linear systems affected by structured uncertainty, and addresses the computation of the robust instability measure defined as the largest sum of the real parts of the unstable eigenvalues over all admissible uncertainties. In particular, it is supposed that the coefficients of the system are affine linear functions of an uncertain vector constrained into a polytope. First, an equivalent reformulation of this robust instability measure into a suitable robust stability margin of a finite family of systems is proposed. Second, a linear matrix inequality (LMI) condition is provided to establish upper bounds of the robust instability measure through the use of homogeneous Lyapunov functions. Third, a sufficient and necessary condition for establishing the optimality of a computed upper bound is proposed. Some numerical examples illustrate the proposed results. © 2013 IEEE.-
dc.languageengen_US
dc.publisherInstitute of Electrical and Electronics Engineers. The Journal's web site is located at http://www.ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000188-
dc.relation.ispartofIEEE Conference on Decision and Control Proceedingsen_US
dc.rightsIEEE Conference on Decision and Control Proceedings. Copyright © Institute of Electrical and Electronics Engineers.-
dc.rights©2013 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.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleMeasuring the instability in continuous-time linear systems with polytopic uncertaintyen_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.doi10.1109/CDC.2013.6760034-
dc.identifier.scopuseid_2-s2.0-84902312222-
dc.identifier.hkuros230394en_US
dc.identifier.spage1131en_US
dc.identifier.epage1136en_US
dc.publisher.placeUnited States-
dc.customcontrol.immutablesml 140822-

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