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Title: H1 and H2 control design for polytopic continuous-time Markov jump linear systems with uncertain transition rates.
Authors: Morais, Cecilia de Freitas
Braga, Marcio Feliciano
Oliveira, Ricardo Coração de Leão Fontoura de
Peres, Pedro Luis Dias
Keywords: Markov jump linear systems
State feedback control
Continuous-time systems
Issue Date: 2015
Citation: MORAIS, C. de F. et al. H1 and H2 control design for polytopic continuous-time Markov jump linear systems with uncertain transition rates. Automatica, Oxford, v. 52, p. 317-321, 2015. Disponível em: <>. Acesso em: 02 out. 2017.
Abstract: This paper investigates the problems of H1 and H2 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 H1 and H2 state feedback control in both mode-independent and modedependent 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.
ISSN:  0005-1098
metadata.dc.rights.license: O periódico Automatica concede permissão para depósito deste artigo no Repositório Institucional da UFOP. Número da licença: 4230720372086.
Appears in Collections:DEELT - Artigos publicados em periódicos

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