Halanay不等式的推广及在时滞神经网络稳定性中的应用

A Generalization of Halanay Inequality and Its Application in Stability of Delayed Neural Networks

建立了一类推广形式的Halanay不等式,并基于此研究了具有不同类型时滞的神经网络渐近稳定性.首先,通过引入?-类函数,并利用反证法,建立了一个时滞微分不等式来推广著名的Halanay不等式,该时滞可以是有界的或无界的,也可以是离散形式或比例形式.作为该不等式的一个应用,进一步讨论了含有不同类型时滞的神经网络渐近稳定性,并建立了稳定性判别准则.最后,通过数值模拟验证了相关理论结果.

A type of generalized Halanay inequality is established and applied to the asymptotic stability analysis of neural networks with different time-delays.Firstly,by introducing?-class functions and using the method of reduction to absurdity,a differential time-delayed inequality is established to generalize the well-known Halanay inequality,where the time-delay can be bounded or infinite,and can be discrete form or proportional form.As an application of the inequality,the asymptotic stability is investigated for neural networks with different types of delays and some stability criteria are derived.Finally,some numerical simulations are provided to verify the theoretical results.