On Stochastic Stabilization of Discrete-Time Markovian Jump Systems with Delay in State

In this paper, we investigate the stochastic stabilization problem for a class of linear discrete time-delay systems with Markovian jump parameters. The jump parameters considered here is modeled by a discrete-time Markov chain. Our attention is focused on the design of linear state feedback memoryless controller such that stochastic stability of the resulting closed-loop system is guaranteed when the system under consideration is either with or without parameter uncertainties. Sufficient conditions are proposed to solve the above problems, which are in terms of a set of solutions of coupled matrix inequalities