A Novel Dead Zone Reaching Law of Discrete-Time Sliding Mode Control with Disturbance Compensation

In this paper, a novel dead zone sliding mode reaching law with disturbance compensation is developed for uncertain discrete-Time systems. The reaching law is established based on the dead zone function and a high-order disturbance compensator, which estimates and compensates the disturbance by the high-order difference function. The exponential function, which is constructed based on the switching function, is employed to regulate the control gains. Different from existing similar works, the presented new reaching law has the ability to obtain a quasi-sliding mode (QSM) with an adjustable order O(T^{n+ 1}) boundary layer. Hence, much smaller ultimate magnitude of the QSM domain (QSMD) can be guaranteed and the chattering can be further mitigated. Moreover, system dynamics in and out the decrement band and the QSMD is theoretically analyzed. Numerical simulations are employed to demonstrate the superiority of the developed new method.