Stochastic H2/H∞ Control with (x,u,v)-dependent Noise

In this paper, finite and infinite horizon stochastic H2/H∞control problems with all state, control input and external disturbance-dependent noise are studied. It is shown that the existence condition of finite horizon stochastic H2/H∞control is equivalent to the solvability of four coupled matrix-valued differential equations, and that of infinite horizon stochastic H2/H∞control is equivalent to the solvability of four coupled matrix-valued algebraic equations.