Prediction schemes for disturbance attenuation of discrete-time linear systems with delayed input and delay-free input

In this article, a predictor is developed for discrete-time linear systems with delayed input and delay-free input to attenuate external disturbances. This predictor is designed to estimate a quantity related to the future state and input. The ultimate bounds of the state of the closed-loop system are derived when the predictor-based state feedback control laws are utilized to this class of delayed systems. Based on the expressions of the ultimate bounds, the disturbance attenuation performance is analyzed for the proposed prediction scheme. Moreover, the robustness to model uncertainties is analyzed when the systems are controlled by the traditional predictor-based and the proposed predictor-based control laws. Finally, three numerical examples are employed to show the effectiveness and the robustness of the proposed predictor.