Stability analysis of some delay differential inequalities with small time delays and its applications
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.
scientific article; zbMATH DE number 6144287