Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps

This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear Itô’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.