TITLE:
Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps
AUTHORS:
Huai-Nian Zhu, Cheng-Ke Zhang, Ning Bin
KEYWORDS:
Stochastic Systems; Differential Games; Markovian Jumps; Stochastic H∞ Control
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.10A,
November
1,
2012
ABSTRACT: This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’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.