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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

H-2 control of discrete-time Markov jump linear systems with uncertain transition probability matrix: improved linear matrix inequality relaxations and multi-simplex modelling

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Author(s):
Morais, Cecilia F. [1] ; Braga, Marcio F. [1] ; Oliveira, Ricardo C. L. F. [1] ; Peres, Pedro L. D. [1]
Total Authors: 4
Affiliation:
[1] Univ Estadual Campinas, UNICAMP, Sch Elect & Comp Engn, BR-13083852 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: IET Control Theory and Applications; v. 7, n. 12, p. 1665-1674, AUG 15 2013.
Web of Science Citations: 22
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. (AU)

FAPESP's process: 11/08312-6 - Discretization and Networked Control of Polytopic Systems with Uncertain Sampling Rates and Delay
Grantee:Marcio Feliciano Braga
Support Opportunities: Scholarships in Brazil - Doctorate