Guaranteed cost H∞ control for stochastic systems with delays

The problem of guaranteed cost H_infin control was considered for uncertain stochastic systems with state and input-delays. Based on linear matrix inequality (LMI) method, Ito formula, and so on, a sufficient condition for the solvability of this problem is obtained. Attention is focused on the design of a linear memoryless state feedback controller, which ensures the closed-loop system is mean-square asymptotically stable, the given quadratic cost function has an upper bound, and a prescribed H_infin performance level is fulfilled for all admissible uncertainties. Finally, a numerical example is provided to demonstrate the proposed method is correct and effective.