Growth estimates and asymptotic stability for a class of differential- delay equation having time-varying delay
type: Item
instance of: scholarly article
title: Growth estimates and asymptotic stability for a class of differential- delay equation having time-varying delay
zbMATH Open document ID: 0755.34071
DOI: 10.1016/0022-247X(92)90127-Y
author: James Louisell
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: Using the technique of Lyapunov functionals the author studies the asymptotic stability of the equation \(\dot x(t)=Ax(t)+Bx(t-h(t))\), where \(x(t)\in\mathbb{R}^ n\). Bounds are derived on the norm of the solution in terms of the behaviour of \(| h'(t)|\) and its average \(a(t)=t^{- 1}\int^ t_ 0| h'(s)| ds\). In particular if \(\liminf_{t\to\infty}a(t)=0\) then each bounded solution \(x\) satisfies \(\liminf_{t\to\infty}| x(t)|=0\).
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 62050
zbMATH Keywords: Lyapunov functionals
zbMATH Keywords: asymptotic stability
zbMATH Keywords: bounded solution
Wikidata QID: Q115364494
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62050