The modelling and numerical simulation of causal non-linear systems

Abstract

To simulate a non-linear system on a digital computer the non-linear mapping from the space of the input signals to the space of the output signals must be represented by a finite arithmetical process. As well as the need to describe elements of the input and output spaces by a finite set of real numbers parameters it is also necessary to find a finite description of the mapping process. For most systems a finite description is not possible and the simulation must be justified by proving an appropriate approximation theorem. Such theorems can be thought of as extensions of the famous Stone-Weierstrass theorem. In this paper we will show that for causal systems defined by a continuous mapping a stable approximation can be constructed using finite arithmetic so that the causal nature of the original system is preserved.