State Observer-Based Predictor Feedback Control for Discrete-Time Linear Systems With State and Input Delays via Fundamental Matrices

The stabilization problem for discrete-time linear systems subject to both state and input delays is addressed when the state variables are not available. Full-order and reduced-order observers with output feedback are designed for state estimation. Then, observer-based predictors with an explicit form are developed to predict future states using fundamental matrices. Next, two classes of state observer-based predictor feedback controllers are proposed to solve the stabilization problem. It is shown that the characteristic polynomial of the closed-loop system under the proposed control law is the product of the characteristic polynomials of the input-delay-free closed-loop system and the state estimation error system. Finally, two examples are employed to validate the effectiveness of the proposed controllers.