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Conference Paper: A gram-SOS approach for robust stability analysis of discrete-time systems with time-varying uncertainty

TitleA gram-SOS approach for robust stability analysis of discrete-time systems with time-varying uncertainty
Authors
KeywordsDiscrete time system
Discrete-time case
Robust asymptotical stabilities
Robust stability analysis
Time varying uncertainties
Time-varying parametric uncertainties
Issue Date2013
PublisherAmerican Automatic Control Council. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000030
Citation
The 2013 American Control Conference (ACC), Washington, DC., 17-19 June 2013. In American Control Conference Proceedings, 2013, p. 5863-5868 How to Cite?
AbstractThis paper addresses the problem of establishing robust asymptotical stability of discrete-time systems affected by time-varying parametric uncertainty. Specifically, it is supposed that the coefficients of the system depend linearly on the uncertainty, and that the uncertainty is confined into a polytope. In the continuous-time case, the problem can be addressed by imposing that the system admits a common homogeneous polynomial Lyapunov function (HPLF) at the vertices of the polytope. Unfortunately, such a strategy cannot be used in the discrete-time case since the derivative of the HPLF is nonlinear in the uncertainty. The problem is addressed in this paper through linear matrix inequalities (LMIs) by proposing a novel method for establishing decrease of the HPLF. This method consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The proposed method provides a condition for robust asymptotical stability that is sufficient for any degree of the HPLF candidate and that includes quadratic robust stability as special case. © 2013 AACC American Automatic Control Council.
Persistent Identifierhttp://hdl.handle.net/10722/184986
ISBN
ISSN

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.date.accessioned2013-07-15T10:22:16Z-
dc.date.available2013-07-15T10:22:16Z-
dc.date.issued2013en_US
dc.identifier.citationThe 2013 American Control Conference (ACC), Washington, DC., 17-19 June 2013. In American Control Conference Proceedings, 2013, p. 5863-5868en_US
dc.identifier.isbn978-1-4799-0178-4-
dc.identifier.issn0743-1619-
dc.identifier.urihttp://hdl.handle.net/10722/184986-
dc.description.abstractThis paper addresses the problem of establishing robust asymptotical stability of discrete-time systems affected by time-varying parametric uncertainty. Specifically, it is supposed that the coefficients of the system depend linearly on the uncertainty, and that the uncertainty is confined into a polytope. In the continuous-time case, the problem can be addressed by imposing that the system admits a common homogeneous polynomial Lyapunov function (HPLF) at the vertices of the polytope. Unfortunately, such a strategy cannot be used in the discrete-time case since the derivative of the HPLF is nonlinear in the uncertainty. The problem is addressed in this paper through linear matrix inequalities (LMIs) by proposing a novel method for establishing decrease of the HPLF. This method consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The proposed method provides a condition for robust asymptotical stability that is sufficient for any degree of the HPLF candidate and that includes quadratic robust stability as special case. © 2013 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.subjectDiscrete time system-
dc.subjectDiscrete-time case-
dc.subjectRobust asymptotical stabilities-
dc.subjectRobust stability analysis-
dc.subjectTime varying uncertainties-
dc.subjectTime-varying parametric uncertainties-
dc.titleA gram-SOS approach for robust stability analysis of discrete-time systems with time-varying 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.scopuseid_2-s2.0-84883548402-
dc.identifier.hkuros216395en_US
dc.identifier.spage5863-
dc.identifier.epage5868-
dc.publisher.placeUnited States-
dc.customcontrol.immutablesml 140122-

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