Synthesized variable structure control and gray prediction for a class of perturbed systems

Based on the Lyapunov stability theorem, we apply a gray prediction scheme to eliminate the “chattering” disadvantage of the traditional variable structure control. By using a moving window of recent past data, we can directly identify the system dynamics and unknown perturbations via the gray prediction scheme. Therefore there is no need for the information of the upper bound of the perturbations in advance. In addition, the presented control scheme ensures the property of the globally uniformly ultimate boundness for the overall controlled system. Finally, a numerical example is given to illustrate the feasibility of the proposed control scheme.