On stability of systems of delay differential equations
type: Item
instance of: scholarly article
title: On stability of systems of delay differential equations
zbMATH Open document ID: 0961.34064
DOI: 10.1016/S0377-0427(99)00337-4
author: Baruch Cahlon
author: Darrell Schmidt
published in: Journal of Computational and Applied Mathematics
publication date: 2001-05-16T00:00:00Z
review text: The authors study a special class of the linear autonomous systems with constant delay of the form \[ \dot x(t)=\alpha Ax(t)+(1-\alpha)Ax(t-\tau), \] where \(A\) is an \(n\times n\)-matrix, \(\tau>0\) is constant, \(0\leq\alpha\leq 1\). Necessary and sufficient conditions for the asymptotic stability of the system are given in terms of the eigenvalues of \(A\). Due to the special form of the system the problem is reduced to systems of first- and second-order problems. The proof of the results are carried out by an application of the well-known Pontryagin criterion on the quasi-polynomial zeros [\textit{L. S.Pontryagin}, Am. Math. Soc., Translat., II. Ser. 1, 95-110 (1955); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 6, 115-134 (1942; Zbl 0068.05803)]. To determine the asymptotic stability four algorithmic tests are given. The paper is provided with two illustrative examples.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 1472303
zbMATH Keywords: linear delay equations
zbMATH Keywords: asymptotic stability criteria
zbMATH Keywords: quasi-polynomials
reviewed by: Oleg Anashkin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1472303