Limiting sampling results for continuous-time ARMA systems

Abstract

The objective of this paper is to present some general properties of discrete-time systems originating from fast sampled continuous-time autoregressive moving average (CARMA) systems. In particular, some results concerning the zero locations and the innovations variance of fast sampled CARMA systems will be stated. Knowledge of these properties is of importance in various fast sampling applications, such as discrete-time simulation of continuous-time systems and identification of continuous-time systems using discrete-time measurements. The main contribution, however, is to provide a mean to evaluate limiting properties for various problems. For example, how to determine the accuracy of approximate sampling schemes, how to describe the characteristics of different estimators, and how to examine the behaviour of the dynamics of a fast sampled system. The results are illustrated by an extensive set of examples.