Variable structure controller design with H∞ norm and variance constraints for stochastic model reference systems

Based on the concept of variable structure control, this paper investigates the design of the controller u(t) to achieve the error state upper bound covariance control with H, norm and variance constraints for a stochastic model reference system. By using the invariance property of variable structure control, the matched reference model input and the plant error term disappear on the sliding mode of the error system. With the aid of the Ito-formula, the controller u(t) is proposed. Combining the sliding phase and hitting phase of variable structure control design, the control feedback gain matrix G is derived to achieve the goals.