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M. A. Rami and X. Y. Zhou, “Linear Matrix Inequalities, Riccati Equations, and Indefinite Stochastic Linear Quadratic Controls,” IEEE Transactions on Automatic Control, Vol. 45, No. 6, 2000, pp. 1131-1143. doi: 10.1109/9.863597

has been cited by the following article:

• 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.