The modelling and numerical simulation of causal non-linear systems

To simulate a non-linear system on a digital computer the non-linear mappin g from the space of input signals to the space of output signals must be re presented 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 number par ameters it is also necessary to find a finite description of the mapping pr ocess. For most systems a finite description is not possible and the simula tion must be justified by proving ail appropriate approximation theorem. Su ch 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 c ontinuous mapping a stable approximation can be constructed using finite ar ithmetic so that the causal nature of the original system is preserved.