On the asymptotic stability of solutions of nonlinear systems with delay
type: Item
instance of: scholarly article
title: On the asymptotic stability of solutions of nonlinear systems with delay
zbMATH Open document ID: 1258.34148
DOI: 10.1134/S0037446612020218
author: Xianqiang Yang
published in: Siberian Mathematical Journal
publication date: 2012-11-14T00:00:00Z
review text: The authors consider two systems of differential equations: ordinary \[ \dot X(t)=F(X(t)),\quad F(0)=0\eqno(1) \] and retarded \[ \dot X(t)=F(X(t-\tau)),\eqno(2) \] where \(X\) is an \(n\)-dimensional vector and the components of \(F(X)\) are homogeneous functions of order \(\mu\geq1\). In the case \(\mu>1\), they prove that the trivial solution of (2) is asymptotically stable for all \(\tau>1\) if the zero solution of equations (1) is asymptotically stable. They estimate the time of transitions, study the influence of perturbations on the stability of the trivial solution, and prove a theorem on the asymptotic stability of a complex system describing the interaction of two nonlinear subsystems.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 6105690
zbMATH Keywords: delay system
zbMATH Keywords: asymptotic stability
zbMATH Keywords: Lyapunov functions
reviewed by: Alexander O. Ignatyev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6105690