Notes on fading-memory conditions
type: Item
instance of: scholarly article
title: Notes on fading-memory conditions
zbMATH Open document ID: 1031.93093
published in: Circuits, Systems, and Signal Processing
publication date: 2004-02-25T00:00:00Z
review text: In some studies concerning the approximation of nonlinear systems, the concept of a weighting function \(w\) plays a central role. This paper, in which attention is focused on continuous-time cases, directs attention to some interesting properties of systems that have \(\mathbb{R}_+\) fading memory or fading memory. In particular, the author shows that half-line input-output maps that have \(\mathbb{R}_+\) fading memory with respect to some \(w\) in fact have \(\mathbb{R}_+\) fading memory with respect to all such \(w\)'s. And it is shown that a similar proposition holds in a setting concerning Volterra-series approximations for continuous-time systems with inputs and outputs defined on all of \(\mathbb{R}\). It is also shown that, in that setting, fading memory is equivalent to uniform fading memory. Some related results are also described.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93A30
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1925614
zbMATH Keywords: nonlinear systems
zbMATH Keywords: weighting function
zbMATH Keywords: fading memory
zbMATH Keywords: input-output maps
zbMATH Keywords: Volterra-series approximations
zbMATH Keywords: continuous-time systems
author: Irwin W. Sandberg
MaRDI profile type: Publication
full work available at URL: s00034-004-7012-6
OpenAlex ID: W1975224572
DOI: 10.1007/S00034-004-7012-6
description: scientific article; zbMATH DE number 1925614