Stabilization of Discrete-Time Systems with Input and Output Delays

Abstract

This chapter studies observer based output feedback control of discrete-time linear systems with both multiple input and output delays. Based on the predictor feedback theory, the TPF approach is established to design the controllers. Two classes of controllers, namely, the memory observer and memoryless observer based controllers, are proposed. For both of these two classes of controllers, both full-order and reduced-order observers are considered. It is shown that the separation principle holds in the memory observer based output feedback scheme and does not hold for the memoryless observer based one. As a result, the stability of the memory observer-based output feedback control system can be proven with the help of the state feedback results established earlier and the stability of the memory observer-based output feedback control systems has to be proven via Lyapunov stability theory. Intricate Lyapunov stability analysis has been carried out for this purpose.