Comparison between explicit and implicit discrete-time implementations of sliding-mode controllers

Different time-discretization methods for sliding-mode control (SMC) are presented. A new discrete-time sliding-mode control scheme is proposed for linear time-invariant (LTI) systems. It is error-free in the discretization of the equivalent part of the control input. Results from simulations using the various discretized SMC schemes are shown, with and without perturbations. They illustrate the different behaviours that can be observed.