Stability criterion for linear systems with nonlinear delayed perturbations
type: Item
instance of: scholarly article
title: Stability criterion for linear systems with nonlinear delayed perturbations
zbMATH Open document ID: 0936.34062
author: Chunhai Hou
author: Furong Gao
author: Jixin Qian
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-05-18T00:00:00Z
review text: An autonomous linear system with nonlinear perturbation and retarded argument \[ x'(t)= Ax(t)+ f(t,x(t- h_1(t)),\dots, x(t- h_n(t))),\quad x\in\mathbb{R}^n,\tag{\(*\)} \] is considered, with \(A\in\mathbb{R}^{n\times n}\), \(0\leq h_i(t)\leq\overline h=\text{const}\), and \(f\) is sublinear. The matrix \(A\) is called quasi-dominant if there exist \(d_i>0\) such that \(d_i a_{ii}> \sum_{j\neq i} d_i|a_{ij}|\). The authors connect with \(A\) a quasi-dominant matrix \(M\). When \(M\) is quasi-dominant then \((*)\) is globally asymptotically stable.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 1346377
zbMATH Keywords: perturbed linear differential equations
zbMATH Keywords: globally asymptotically stable solutions
zbMATH Keywords: nonlinear perturbation
reviewed by: Tadeusz Dłotko
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6490
OpenAlex ID: W2084688151
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DOI: 10.1006/JMAA.1999.6490
description: scientific article; zbMATH DE number 1346377