Sliding mode controllers design for linear discrete-time systems with matching perturbations

A simple methodology for designing sliding mode controllers is proposed in this paper for a class of linear multi-input discrete-time systems with matching perturbations. If the functions of perturbations are bounded, the proposed controllers cannot only satisfy the discrete sliding condition, but also drive the state trajectories toward a small bounded region, whose bound is dependent on the magnitude of perturbations. In order to stabilize the closed-loop system, the determination of designed parameter of controllers is discussed. Neither chattering phenomenon will occur nor the knowledge of upper bound of perturbations is required. Numerical example is also given for demonstrating the feasibility of the proposed control scheme.