Stochastic stabilization of a class of nonhomogeneous Markovian jump linear systems

This paper deals with the problem of stochastic stability analysis and control synthesis of a class of Markovian jump linear systems (MJLS) with time-varying transition probabilities (TPs) in the discrete-time domain. The time-varying character is considered to be in a polytopic sense. The approach followed in this note is based on the use of a parameter dependent stochastic Lyapunov function. We give a stability condition in terms of a linear matrix inequality (LMI) feasibility problem. The obtained results are illustrated in a numerical example.