H∞ control for discrete-time linear systems with Markovian jumping parameters

We investigate the problem of H_∞ control for a class of linear discrete-time systems with Markovian jumping parameters. The jumping parameters considered here are discrete-time Markov processes. Our attention is focused on the design of a linear state feedback controller such that both stochastic stability and a prescribed H_∞ performance are required to be achieved. Furthermore, the robust H_∞ control problem for Markovian jumping systems with parameter uncertainties are also studied. Some sufficient conditions are proposed to solve the above problems, which are in terms of a set of solutions of coupled algebraic Riccati equations