Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations
type: Item
instance of: scholarly article
title: Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations
zbMATH Open document ID: 1065.34076
published in: Applied Mathematics and Computation
publication date: 2005-02-22T00:00:00Z
review text: This paper is concerned with the asymptotic stability of the delay differential systems of neutral type \[ x'(t) - C x'(t-\tau_2)= A x(t) + B x(t-\tau_1)+ f_1(t,x(t))+f_2(t,x(t-\tau_1), \quad t \geq 0, \tag \(*\) \] where \( \tau_1, \tau_2\) are positive constant delays, \( A,B,C\) constant real matrices of appropriate dimensions, and the nonlinear functions \( f_i\) satisfy \( \| f_i(t,u) \| \leq \alpha_i \| u \|\), \(i=1,2\), for some scalars \( \alpha_i\). For system \((*)\), the author gives sufficient conditions on the matrix coefficients that imply the asymptotic stability of the zero solution. The main advantage of the present result is that the sufficient conditions for stability can be checked by means of a convex optimization algorithm whereas other stability criteria are expressed in terms of matrix norms and turn out to be more conservative. Some examples of two-dimensional problems are presented in which the stability is tested by using Matlab's LMI Control Toolbox.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 2136194
zbMATH Keywords: delay differerential systems
zbMATH Keywords: neutral systems
zbMATH Keywords: asymptoric stability
author: Ju H. Park
describes a project that uses: Matlab
describes a project that uses: LMI toolbox
MaRDI profile type: Publication
full work available at URL: j.amc.2003.12.036
OpenAlex ID: W2145043167
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DOI: 10.1016/J.AMC.2003.12.036
description: scientific article; zbMATH DE number 2136194