On generalized linear regular delay systems
type: Item
instance of: scholarly article
title: On generalized linear regular delay systems
zbMATH Open document ID: 0933.34071
author: I. G. Stratis
author: Grigoris I. Kalogeropoulos
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-12-05T00:00:00Z
review text: The authors consider generalized linear regular delay systems of the form \[ Ex'(t)=Ax(t-r)+Bu(t), \quad t>t_0,\;r>0, \qquad x(t)=\phi(t), \quad t_0-r\leq t \leq t_0, \tag{1} \] with \(E,A\in \mathbb{R} ^{n\times n}\), \(B\in \mathbb{R} ^{n\times l}\), \(u\in C([t_0, +\infty))\), \(\phi\in C([t_0-r,t_0))\). The matrices \(E\) and \(A\) may be degenerated but the matrix pencil \(sE-A\) is supposed to be regular. First, system (1) is reduced to a suitable homogeneous one. Then the homogeneous system is decomposed in two subsystems, whose solutions are obtained. The conditions on the function \(\phi\) are presented for initial value problem (1) to have a unique solution. The main tools are the matrix pencil theory and the theory of systems of linear delay differential equations. Some necessary preliminaries from these theories are also included.
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 1346374
zbMATH Keywords: matrix pencil theory
zbMATH Keywords: generalized regular linear delay systems
zbMATH Keywords: Weierstrass canonical form
reviewed by: S. Yanchuk
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6458
OpenAlex ID: W4210484134
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DOI: 10.1006/JMAA.1999.6458
description: scientific article; zbMATH DE number 1346374