ℋ∞ state feedback control for MJLS with uncertain probabilities. (February 2015)

• Record Type: Journal Article
• Authors: Morais, Cecília F.; Braga, Márcio F.; Oliveira, Ricardo C.L.F.; Peres, Pedro L.D.
• Is Part Of: Automatica. Volume 52(2015)
• Page Start: 317
• Page End: 321
• Publication Date: 2015-02
• Subjects: Markov jump linear systems -- Discrete-time -- Uncertain transition probability -- ℋ∞ state feedback control -- Linear matrix inequalities (LMIs); Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2014.12.013
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper addresses the problem of ℋ ∞ state feedback control design for discrete-time Markov jump linear systems (MJLS) with uncertain transition probability matrix. The main novelty is that, differently from the existing approaches in the literature, the proposed conditions allow the use of polynomially parameter-dependent Lyapunov matrices to certify the closed-loop stability of the MJLS. Therefore, the method is able to provide ℋ ∞ controllers in cases where the other techniques fail. The synthesis conditions are given in terms of linear matrix inequality relaxations. Examples illustrate the main advantages of the proposed control design method when compared to other approaches from the literature.