Robust H∞ control for uncertain singular systems with state delay and Brownian motion

This note deals with the problem of robust H_infin control for uncertain singular stochastic systems with state delay and Brownian motion. The state feedback control laws are designed to guarantee that the resulting closed-loop system is regular, impulse-free and mean-square asymptotically stable for all admissible uncertainties. And a prescribed H_infin performance is achieved in the robust H_infin control problem. This criteria is devised in terms of parameters weak coupled LMI equations (PWCLMIE). At the same time, free-weighting matrices are introduced into PWCLMIE. So we gain control law with large time-delay and small disturbance attenuation. A numerical example is given to demonstrate the effectiveness of the proposed criteria.