Stochastic zero-sum differential games and H∞ control of discrete-time Markov jump systems

In this paper, linear quadratic stochastic zero-sum differential games for discrete-time Markov jump systems are discussed. It is shown that the existence condition of finite horizon stochastic zero-sum games is equivalent to the solvability of the associated difference Riccati equations, and that of infinite horizon stochastic zero-sum games is equivalent to the solvability of the associated algebraic Riccati equations. Moreover, the explicit expressions of the optimal strategies are constructed. The results are applied to H_∞ control problem for discrete-time Markov jump systems.