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This paper proposes a multi-power reaching law-based sliding-mode control (SMC) for uncertain discrete-time systems. The proposed controller mainly consists of the multi-power function along with the perturbation estimation. Different from the existing similar works, the control gains of the controller are adaptively adjusted by the multi-power function, i.e., three power terms, according to different stages of the convergence process. Hence, the system trajectory of the controlled system can be forced toward the sliding surface with a faster convergence rate. The corresponding sliding-mode dynamics and the reaching steps to the sliding surface are theoretically analyzed. A practical example is given to examining the validity of the proposed method. The simulation results show that the proposed method reduces the reaching steps while guaranteeing better control accuracy than the single power method.

Multi-Power Reaching Law Based Discrete-Time Sliding-Mode Control