Finite horizon stochastic H2/H∞ control with discrete and distributed delays

Based on a Lyapunov–Krasovskii functional, a new delay-dependent H∞ performance criterion is established for stochastic systems with discrete and distributed delays. It is shown that the H∞-performance of the corresponding uncontrolled stochastic perturbed system is equivalent to the existence and uniqueness of solutions to the finite horizon stochastic H2/H∞ control problem. The resulting H2/H∞ controller is characterised by a kind of generalized forward–backward stochastic differential equations with delayed stochastic differential equations as forward equations and generalized anticipated backward stochastic differential equations as backward equations. A practical example is given to illustrate the proposed method.