Stabilization of Linear Discrete-time Systems With Multiple Input and Output Delays by Observer-based Delayed Output Feedback

This work studies the stabilization of linear discrete-time time-delay systems by observer-based delayed output feedback (DOF). By introducing DOF to construct the observer error of a full-order observer, we develop a novel observer, which can estimate (predict) the (future) states in a deadbeat manner for any observer gain. Based on the observer developed, we design an observer-based DOF controller, which stabilizes the system asymptotically and makes the closed-loop system act like delay-free. To reduce the computation cost, another observer-based DOF method is presented for systems with a single input delay and multiple output delays. Finally, a numerical example illustrates the effectiveness of the proposed methods.