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Type: Artigo
Title: ℋ∞ and ℋ2 control design for polytopic continuous-time Markov jump linear systems with uncertain transition rates
Author: Morais, Cecília F.
Braga, Márcio F.
Oliveira, Ricardo C. L. F.
Peres, Pedro L. D.
Abstract: This paper investigates the problems of urn:x-wiley:rnc:media:rnc3329:rnc3329-math-0007 and urn:x-wiley:rnc:media:rnc3329:rnc3329-math-0008 state feedback control design for continuous‐time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi‐simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter‐dependent Lyapunov matrices to certify the mean square closed‐loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope with urn:x-wiley:rnc:media:rnc3329:rnc3329-math-0009 and urn:x-wiley:rnc:media:rnc3329:rnc3329-math-0010 state feedback control in both mode‐independent and mode‐dependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with other techniques from the literature
Subject: Desigualdades matriciais lineares
Country: Reino Unido
Editor: John Wiley & Sons
Rights: Fechado
Identifier DOI: 10.1002/rnc.3329
Date Issue: 2016
Appears in Collections:FEEC - Artigos e Outros Documentos

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