ℋ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain transition probability matrix

This paper investigates the problem of ℋ_∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the transition probability matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ_∞ bound for the discrete-time MJLS. The proposed conditions are based on linear matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ_∞ guaranteed cost. The proposed strategy can also cope with ℋ_∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.