Predictor-based composite disturbance rejection control for discrete-time linear systems with input delay and disturbance

In this paper, a new composite disturbance rejection control approach is proposed for a class of discrete-time systems with input delays and mutational disturbances. To deal with the input delay, a predicted state is designed and then the original system is transformed into a delay-free auxiliary system with unknown future disturbance. By designing a new Lagrange-interpolation-polynomial-based predictor, the disturbance is predicted, and the proposed predictor provides a fast convergence speed and the prediction error is small. Besides, to identify the unknown mutational points, a mutational points identification (MPI) strategy is proposed, based on which the composite disturbance rejection controller is further designed by combining a new discrete-time sliding mode controller and the disturbance predictor. It is shown that under proposed controller, system state will converge to a small region, and the deviations caused by the mutational points are bounded. Finally, the simulations illustrate the advantages of the proposed approach.