Asymptotic stability of solutions of a class of systems of nonlinear differential equations with delay
type: Item
instance of: scholarly article
title: Asymptotic stability of solutions of a class of systems of nonlinear differential equations with delay
zbMATH Open document ID: 1259.34063
DOI: 10.3103/S1066369X12050015
author: Xianqiang Yang
published in: Russian Mathematics
publication date: 2012-11-20T00:00:00Z
review text: The authors study systems of differential equations with delay whose right-hand sides are represented as sums of potential and gyroscopic components of vector fields. They assume that, in the absence of delay, zero solutions of the considered systems are asymptotically stable. By Lyapunov's direct method, using the Razumikhin approach, they prove that, in the case of essentially nonlinear equations, the asymptotic stability of the zero solution is preserved for any value of the delay. The duration of the transient processes for asymptotically stable systems with delay is estimated. The stability of the perturbed systems is studied.
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 6108809
zbMATH Keywords: delay systems
zbMATH Keywords: asymptotic stability
zbMATH Keywords: Lyapunov functions
reviewed by: Alexander O. Ignatyev
MaRDI profile type: Publication
cites work: Theory of functional differential equations. 2nd ed
cites work: Q4779786
cites work: Q3904472
cites work: Asymptotic stability of solutions to systems of nonstationary differential equations with homogeneous right-hand sides
description: scientific article; zbMATH DE number 6108809