LINEAR-QUADRATIC STOCHASTIC DIFFERENTIAL GAMES WITH MARKOV JUMPS AND MULTIPLICATIVE NOISE: INFINITE-TIME CASE

This paper discusses the linear quadratic (LQ) differential games for stochastic systems with Markov jumps and multiplicative noise in infinite-time case. Firstly, we consider zero-sum games for stochastic systems with multiplicative noise. Here the state weighting matrix is allowed to be indefinite, and an important theorem is gained. Further, we discuss the LQ differential games for stochastic systems with Markov jumps and multiplicative noise. We introduce the important definition of stochastic detectability, which has close relation to Lyapunov equation. Based on Lyapunov equation, we obtain four-coupled generalized algebraic Riccati equations (GAREs), which are essential on finding the optimal strategies (Nash equilibrium strategies) and the optimal cost values for infinite stochastic differential games. Finally, the corresponding simulation examples are presented to illustrate the main results.