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Article: H∞ and H2 norms of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functions

TitleH∞ and H2 norms of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functions
Authors
Issue Date2015
PublisherIEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
Citation
IEEE Transactions on Automatic Control, 2015, v. 60 n. 10, p. 2614-2625 How to Cite?
AbstractThis paper addresses the problem of determining the H∞ and H2 norms of 2-D mixed continuous-discrete-time systems. The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs). The second contribution is to show that the upper bounds provided are nonconservative by using Lyapunov functions in the chosen class with sufficiently large degree. The third contribution is to provide conditions for establishing the tightness of the upper bounds. The fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient LMI condition for establishing positive semidefiniteness of even Hermitian matrix polynomials. This result is also exploited to derive an improved necessary and sufficient LMI condition for establishing exponential stability of 2-D mixed continuous-discrete-time systems. Some numerical examples illustrate the proposed approach. It is worth remarking that nonconservative LMI methods for determining the H∞and H2 norms of 2-D mixed continuous-discrete-time systems have not been proposed yet in the literature.
Persistent Identifierhttp://hdl.handle.net/10722/227287
ISSN
2015 Impact Factor: 2.777
2015 SCImago Journal Rankings: 4.238

 

DC FieldValueLanguage
dc.contributor.authorChesi, G-
dc.contributor.authorMiddleton, RH-
dc.date.accessioned2016-07-18T09:09:34Z-
dc.date.available2016-07-18T09:09:34Z-
dc.date.issued2015-
dc.identifier.citationIEEE Transactions on Automatic Control, 2015, v. 60 n. 10, p. 2614-2625-
dc.identifier.issn0018-9286-
dc.identifier.urihttp://hdl.handle.net/10722/227287-
dc.description.abstractThis paper addresses the problem of determining the H∞ and H2 norms of 2-D mixed continuous-discrete-time systems. The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs). The second contribution is to show that the upper bounds provided are nonconservative by using Lyapunov functions in the chosen class with sufficiently large degree. The third contribution is to provide conditions for establishing the tightness of the upper bounds. The fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient LMI condition for establishing positive semidefiniteness of even Hermitian matrix polynomials. This result is also exploited to derive an improved necessary and sufficient LMI condition for establishing exponential stability of 2-D mixed continuous-discrete-time systems. Some numerical examples illustrate the proposed approach. It is worth remarking that nonconservative LMI methods for determining the H∞and H2 norms of 2-D mixed continuous-discrete-time systems have not been proposed yet in the literature.-
dc.languageeng-
dc.publisherIEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9-
dc.relation.ispartofIEEE Transactions on Automatic Control-
dc.rightsIEEE Transactions on Automatic Control. Copyright © IEEE.-
dc.rights©2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleH∞ and H2 norms of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functions-
dc.typeArticle-
dc.identifier.emailChesi, G: chesi@eee.hku.hk-
dc.identifier.authorityChesi, G=rp00100-
dc.description.naturepostprint-
dc.identifier.doi10.1109/TAC.2015.2404491-
dc.identifier.hkuros259214-
dc.identifier.volume60-
dc.identifier.issue10-
dc.identifier.spage2614-
dc.identifier.epage2625-
dc.publisher.placeUnited States-

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