Abstract
This paper investigates the necessity of the internal model principle for the so-called repetitive control systems. The paper demonstrates that the commonly accomodated “periodic function generator” which makes use of a puredelay operatox is necessary for realization of repetitive control systems. This is done via an effective use of the realization theory for pseudo-rational impulse responses developed by the first author. Then stabilizability of repetitive control systems is considered, and it is proved that the current restriction on the plant, namely the 0-relative degree property, is inevitable for the precise realization of repetitive control. The study is expected to offer a rigid ground for the study of repetitive control systems.
