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Type: Journal article
Title: The modelling and numerical simulation of causal non-linear systems
Author: Howlett, Phil G.
Torokhti, Anatoli P.
Pearce, Charles Edward Miller
Citation: Nonlinear Analysis-Theory Methods and Applications, 2001; 47 (8):5559-5572
Publisher: Elsevier
Issue Date: 2001
ISSN: 0362-546X
School/Discipline: School of Mathematical Sciences : Applied Mathematics
Statement of
P. D. Howlett, A. P. Torokhti and C. E. M. Pearce
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.
Keywords: Causal operators, non-linear systems, Stone-Weierstrass theorem
DOI: 10.1016/S0362-546X(01)00659-9
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Appears in Collections:Applied Mathematics publications

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