Stochastic stability for discrete-time Markov jump Lur´e systems

This paper analyzes the stochastic stability problem of discrete-time Markov jump Lur´e systems. We consider that the switching parameter defining the active mode for both the linear and the cone-bounded nonlinearity is governed by a finite state Markov chain. Based on Linear Matrix Inequalities (LMIs), sufficient conditions are provided for the stability analysis, considering two different assumptions for the transition probability matrix: the case in which it is supposed to be known and the case in which it is supposed to be partially known. As the main tool we employ a stochastic Lur´e type Lyapunov function using the sector condition assumption for the nonlinearities. An academic example is presented in order to illustrate the proposed methods.