CONVERGENT LMI RELAXATIONS FOR ROBUST ANALYSIS OF UNCERTAIN DISCRETE-TIME MARKOV JUMP LINEAR SYSTEMS

The robust stability analysis of discrete-time Markov jump linear systems whose probability matrix is not precisely known, but belongs to a polytopic domain, is investigated in this paper. The robust stability tests are given in terms of a sequence of sufficient LMI conditions based on homogeneous polynomial parameter-dependent Lyapunov matrices of arbitrary degree g on the uncertain parameters. As the degree g increases, the necessary conditions are attained. Numerical examples illustrate the efficiency of the proposed approach when compared with other methods from the literature.