Linear quadratic differential games for discrete-times Markovian jump stochastic linear systems: Infinite-horizon case

This paper deals with the infinite horizon linear quadratic differential games for discrete-time Markovian jump stochastic linear systems with finite number of jump times. By using the relation between the stability of discrete-time Markovian jump stochastic linear systems and the Lyapunov equation, a theorem is derived on finding the optimal strategies and the optimal cost values for infinite horizon stochastic differential games is derived. It is also indicated that the solutions of infinite horizon linear quadratic stochastic differential games are associated with four coupled generalized algebraic Riccati equations. Furthermore, an iterative algorithm is proposed to solve the four coupled generalized algebraic Riccati equations.