Stability analysis of some delay differential inequalities with small time delays and its applications
type: Item
instance of: scholarly article
title: Stability analysis of some delay differential inequalities with small time delays and its applications
zbMATH Open document ID: 1276.34066
author: Bo Liu
author: Wenlian Lu
author: Tianping Chen
published in: Neural Networks
publication date: 2013-03-13T00:00:00Z
review text: The authors consider linear delay differential inequalities with time varying coefficients and a time delay \(\tau >0.\) Considering results obtained in previous papers they relax some conditions to obtain better results. Following Baker and Tang (1996), they weaken a result proved by them under the hypothesis \[ -a(t)+b(t) \leq - \sigma <0, \] to \[ \int_{t_0+nT}^{t_0+(n+1)T} a(t)-b(t)\,dt \geq \delta \] for some \(t_0>0,~T>0\) and \(\delta >0\), \(n=1,2,3,\dots\), which means that it is sufficient to verify the conditions in an average sense. In this set-up, they obtain criteria for the asymptotic stability of the considered system. They apply these results to Hopfield neural networks with time delay. Further, an example involving the consensus algorithm dealing with consensus analysis in networks of multiagents with time varying coupling and delays is also given.
reviewed by: J. Vasundhara Devi
Mathematics Subject Classification ID: 34K38
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 6144287
zbMATH Keywords: delay differential inequality
zbMATH Keywords: time varying systems
zbMATH Keywords: asymptotic stability
zbMATH Keywords: neural networks.
Wikidata QID: Q51373566
MaRDI profile type: Publication
full work available at URL: j.neunet.2012.03.009
OpenAlex ID: W2032674963
cites work: Global almost sure self-synchronization of Hopfield neural networks with randomly switching connections
cites work: Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays
cites work: On global asymptotic stability of neural networks with discrete and distributed delays
cites work: Generalized Halanay inequalities for dissipativity of Volterra functional differential equations
DOI: 10.1016/J.NEUNET.2012.03.009
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description: scientific article; zbMATH DE number 6144287