Stable Zeros of Sampled Systems

Abstract

When a continuous-time system is sampled by use of a zero order holder, all stable poles are transformed into the unit circle. However, there is no simple relation between the zeros of a continuous-time system and its sampled version.
In this paper, a necessary and sufficient condition for stable zeros of a sampled system is presented when a continuous-time system has a strictly proper and rational transfer function. The criterion derived in this paper is represented in terms of coefficients of a continuous-time transfer function and of a sampling period. Further, this paper gives a necessary and sufficient condition which ensures that all zeros of a sampled system are inside the unit circle for all sampling periods.