Some remarks on infinite horizon stochastic H2/H∞ control with (x,u,v)-dependent noise and Markov jumps

This paper investigates the infinite horizon H2/H∞ control problem for stochastic systems with (x,u,v)-dependent noise and Markov jumps. Under the condition of exact detectability, a necessary and sufficient condition for the infinite horizon stochastic H2/H∞ control is derived in terms of four sets of coupled matrix-valued equations. The relationship between the infinite horizon H2/H∞ control and the Nash equilibrium point is discussed when disturbance does or does not enter into the diffusion term. Moreover, a heuristic iteration algorithm is proposed to solve coupled stochastic Riccati equations for the first time.