Characterization of All Causal Internally Stabilizing Repetitive Controllers for Minimum Phase Systems

Abstract

In the present paper, we examine the characterization for the class of all causal internally stabilizing repetitive controllers for linear minimum phase systems. Yamada and Okuyama gave the characterization of all causal stabilizing controllers for linear minimum phase systems. However, their repetitive compensator has limitations, such that the numerator of the repetitive compensator is a biproper rational function. In addition, their characterization includes controllers such that the control system is not internally stable; that is, the transfer function from any exogenous signals to any signal in the control system is not always causal. The purpose of the present paper is to extend the result of Yamada and Okuyama and give the characterization of all causal internally stabilizing controllers, for minimum phase systems, that have more general repetitive compensators.