Delay compensation of discrete-time linear systems by nested prediction

In this study, the authors study the input delay compensation problem for discrete-time linear systems with both state and input delays. Under the assumption that the original time-delay system without input delay can be stabilised by state feedback, a nested predictor feedback controller is established to predict the future states such that the arbitrarily large yet exactly known input delay in the original system is completely compensated. Consequently, it is shown that the closed-loop system consisting of the original time delay system and the nested prediction feedback controller is asymptotically stable. Under an additional assumption, an explicit nested predictor feedback controller without involving any nested summations is also established. Finally, two numerical examples are carried out to illustrate the obtained theoretical results.