Variable structure multiple indices consistency control of stochastic system

This paper considers the problem of designing a variable structure control (VSC) of linear stochastic system which satisfies multiple indices of closed-loop system. On the sliding phase, the equivalent control of VSC of stochastic systems is designed. The feedback gain is calculated to guarantee that the poles of closed-loop system are allocated in specified sector region, disturbance H-infinity is constrained in the specified perturb degree via linear matrix inequality and satisfactory control theory. So the stable state covariance of closed loop system could be in the given permitted range. The tendency law is proposed to satisfy requirement of reaching onto the sliding surface. A numeric example is given to show the effective of the proposed approach.