Static output feedback H2/H∞ control of infinite horizon Markov jump linear stochastic systems with multiple decision makers

In this paper, we discuss infinite-horizon H₂/H_∞ control problem for Markov jump linear stochastic system governed by Itô differential equation with state, control and external disturbance dependent noise involving multiple decision makers. The state and static output feedback strategies are both considered. It is shown that equilibrium conditions are established by the set of cross-coupled stochastic algebraic Riccati equations (CSAREs) for the first time. Furthermore, a necessary condition for the existence of the strategy set is discussed. In particular, it is noteworthy that our new results completely involve some existing results on stochastic H₂/H_∞ control for linear case in the sense that the multiple decision makers and state, control and disturbance dependent noise are considered. Finally, a numerical example to verify the efficiency of the proposed algorithms is given.