A stochastic control of discrete variable structure tracking systems with minimax weighted sensitivity

In this paper, a finite-time step to reach the switching surface for the discrete-time stochastic systems was first obtained by an equivalent control. Owing to the presence of the total disturbance including random disturbance, which is modeled by a stochastic model, and nonlinear time-varying uncertainties, a poor response often occurred. In this situation, an equivalent control obtained by the simultaneous minimization of the weighted sensitivity function in H^∞-norm space between total disturbance and switching surface was employed to attenuate its effect. In addition, a suitable weighting function could partially reject nonlinear time-varying uncertainties, e.g., constant, ramp, sinusoidal uncertainties. For further enhancing system performance, a switching control was designed. In summary, the proposed control (stochastic variable structure tracking control, SVSTC) could deal with the total disturbance that was not necessarily stationary or bounded, the system that was not necessarily minimum phase.