Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/79980
Type: Artigo de periódico
Title: H-2 control of discrete-time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi-simplex modelling
Author: Morais, CF
Braga, MF
Oliveira, RCLF
Peres, PLD
Abstract: This study is concerned with the problem of H-2 state-feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the transition probability matrix is not precisely known, but belongs to a polytopic domain, or contains unknown or bounded elements. As a first contribution, the uncertainties of the transition probability matrix are modelled in terms of the Cartesian product of simplexes, called multi-simplex. Thanks to this representation, the problem of robust mean square stability analysis with an H-2 norm bound can be solved through convergent linear matrix inequality (LMI) relaxations constructed in terms of polynomial solutions. The proposed conditions yield a better trade-off between precision and computational effort when compared with other methods. As a second contribution, new conditions in terms of LMIs with a scalar parameter lying in the interval (-1, 1) are proposed for H-2 state-feedback control with complete, partial or no observation of the Markov chain. Owing to the presence of the scalar parameter, less conservative results when compared with other conditions available in the literature can be obtained, at the price of increasing the associated computational effort. Numerical examples illustrate the advantages of the proposed methodology.
Subject: control system synthesis
discrete time systems
linear matrix inequalities
linear systems
Markov processes
mean square error methods
stability
state feedback
uncertain systems
H-2 control
a'<(2) control
discrete-time Markov jump linear systems
uncertain transition probability matrix
multisimplex modelling
MJLS
LMI
polytopic domain
Cartesian product
robust mean square stability analysis
convergent linear matrix inequality relaxations
polynomial solutions
precision effort
computational effort
scalar parameter
state-feedback control design
Country: Inglaterra
Editor: Inst Engineering Technology-iet
Rights: fechado
Identifier DOI: 10.1049/iet-cta.2012.1015
Date Issue: 2013
Appears in Collections:Unicamp - Artigos e Outros Documentos

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