A Novel Reaching Law for Sliding Mode Control of Uncertain Discrete-Time Systems

This paper proposed a new sliding mode control algorithm for discrete-time systems with matched uncertainty. The new control algorithm is characterized by a new discrete switching surface. Although the exponential reaching law can reduce oscillation, the control effectiveness will be suppressed when the rate of change of disturbance is high. The exponential reaching law cannot force the system states to approach sliding surface s k = 0. In order to solve the contradiction between guaranteeing the basic property of quasi-sliding mode and reducing oscillation, a new discrete reaching law is proposed to improve the reaching process of discrete exponent reaching laws. The proposed method not only can force system state to approach the sliding surface s k = 0 in less width of the switching manifold than existing studies, but also can alleviate chattering when the system representative points are near zero point. Simulation results are provided to validate the feasibility and reasonability of the method.