Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed-loop system possesses the same characteristic equation as the closed-loop system without distinct input delays. Both continuous-time and discrete-time time-delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous-time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.