Robust discrete variable structure control with finite-time approach to switching surface

By using a dead-beat control technique of discrete-time systems, a robust discrete variable structure control (DVSC) is developed for the linear discrete-time systems subject to input disturbance, measurement noise and uncertainty. The proposed control includes two parts: equivalent control and switching control. Based on the internal model principle, the input disturbance and the measurement noise modeled as pulse transfer functions, are rejected by the equivalent control. The unmatched uncertainty caused by the time-invariant parameter variations is also tackled by the equivalent control. If the inverse of stable characteristic polynomial of the real closed-loop system is a finite-degree polynomial, the trajectory reaches the switching surface in a finite-time step. Due to the subjection of input disturbance or measurement noise or uncertainty, a poor response occurs. Under these circumstances, a switching control based on Lyapunov redesign is employed to improve the system performance. The stability of the closed-loop system is then verified by Lyapunov stability theory. Simulations are also given to confirm the usefulness of the proposed controller.