Delay-dependent stability of two-dimensional Markovian jump systems in the Roesser model with interval time-varying delays

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional Markovian jump systems (2D MJSs) described by the Roesser model. The systems under consideration are subject to interval time-varying and full known transition probabilities of the jumping process/Markov chain. First, new finite-sum inequalities are proposed in this paper. Then giving the Lyapunov-Krasovskii functional (LKF) with time-delay and differencing it via new finite-sum inequalities, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.