Discrete-time Sliding Mode Control with Adaptive Reaching Law via Implicit Euler Method

In this paper, a novel adaptive reaching law-based discrete-time sliding mode control scheme is designed and analyzed for nonlinear disturbed systems. The higher-order sliding mode surface is used to obtain the homogeneous asymptotic accuracy of system states. The implicit Euler method is applied to the design of discrete reaching law for the first time, further to completely eliminate numerical chattering. Meanwhile, with the help of a high-order disturbance compensator, the widths of the quasi sliding mode band and attractiveness region are reduced to an adjustable order. The designed adaptive gain functions in the reaching law are able to decrease the reaching time without affecting the accuracy of sliding mode, and the finite number of steps for any initial state to enter the quasi sliding mode band is acquired. Simulation results on magnetic suspension systems are presented to validate the developed method.