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The optimal  L2 - L∞  control problem of a class of uncertain stochastic systems with Wiener process disturbances is studied. Based on the robust  L2 - L∞  control theory, it gives a sufficient condition to solve the resilient controller such that the stochastic system is stochastically stabilizable and satisfies the given  L2 - L∞  control performance index. By constructing an appropriate Lyapunov-Krasovskii functional and applying linear matrix inequalities techniques, the  L2 - L∞  controller design problem is derived and then described as an optimization one. Simulation results are given to demonstrate the validity of the proposed approach.

Robust L 2 - L ∞ Controller Design of a Class of Uncertain Stochastic Systems with Wiener Process Disturbances