Some remarks on infinite horizon stochastic [formula omitted] control with [formula omitted] noise and Markov jumps.

This paper investigates the infinite horizon H 2 / 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 H 2 / H ∞ control is derived in terms of four sets of coupled matrix-valued equations. The relationship between the infinite horizon H 2 / 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. [ABSTRACT FROM AUTHOR]