On linear models for nonlinear systems
type: Item
instance of: scholarly article
title: On linear models for nonlinear systems
zbMATH Open document ID: 1017.93023
DOI: 10.1016/S0005-1098(02)00183-8
published in: Automatica
publication date: 2003-02-13T00:00:00Z
review text: Best linear time-invariant (LTI) approximations are analyzed for several interesting classes of discrete nonlinear time-invariant systems. These include nonlinear finite impulse response systems and a class of nonsmooth systems called bi-gain systems. The Fréchet derivative of a smooth nonlinear system is studied as a potential good LTI model candidate. The Fréchet derivative is determined for nonlinear finite memory systems and for a class of Wiener systems. Most of the concrete results are derived in an \(\ell_\infty\) signal setting. Applications to linear controller design, to identification of linear models and to the estimation of the size of the unmodelled dynamics are discussed.
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93A30
Mathematics Subject Classification ID: 93B18
zbMATH DE Number: 1868216
zbMATH Keywords: approximation
zbMATH Keywords: discrete-time systems
zbMATH Keywords: Fréchet derivative
zbMATH Keywords: linear models
zbMATH Keywords: nonlinear systems
zbMATH Keywords: system identification
zbMATH Keywords: Wiener systems
zbMATH Keywords: nonsmooth systems
zbMATH Keywords: bi-gain systems
zbMATH Keywords: finite memory systems
zbMATH Keywords: \(\ell_\infty\) signal setting
author: P. M. Mäkilä
author: Jonathan R. Partington
MaRDI profile type: Publication
Wikidata QID: Q56319381
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full work available at URL: s0005-1098(02)00183-8
OpenAlex ID: W2048127398
description: scientific article; zbMATH DE number 1868216