Finite-dimensional representation of delay systems
type: Item
instance of: scholarly article
title: Finite-dimensional representation of delay systems
zbMATH Open document ID: 1002.93027
DOI: 10.1016/S0893-9659(02)80002-7
published in: Applied Mathematics Letters
publication date: 2002-08-15T00:00:00Z
review text: The author considers the state delayed system \[ \dot x(t)= A_0 x(t)+ A_1 x(t-\tau)+ B_0 u(t),\quad x_0= \varphi,\tag{1} \] where \(\varphi\in C([-r, 0]; \mathbb{R}^n)\), \(A_0, A_1\in \mathbb{R}^{n\times n}\), \(B_0\in \mathbb{R}^{n\times m}\), \(u(t)\in \mathbb{R}^m\), \(x(t)\in \mathbb{R}^n\). It is shown that one can construct a finite-dimensional system whose partial state replicates the response of the delay system (1) up to small solutions of the homogeneous delayed system.
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 93B11
zbMATH DE Number: 1781914
zbMATH Keywords: system approximation
zbMATH Keywords: state delayed system
author: Y. A. Fiagbedzi
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
cites work: Introduction to functional differential equations
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full work available at URL: s0893-9659(02)80002-7
OpenAlex ID: W1973658610
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description: scientific article; zbMATH DE number 1781914