Asymptotical Stability and Exponential Stability in Mean Square of Impulsive Stochastic Time-Varying Neural Network

The effect of impulse on stability of neural network is evident not only in performance, that is, impulsive control and impulsive interference. The amount of impulse has a certain impact on stability of neural network. Unlike traditional average impulsive interval, a new strategy is applied in this paper, namely, impulsive density. Based on this strategy, by constructing Lyapunov function, we establish sufficient conditions for mean square asymptotical stability of impulsive stochastic time-varying neural network without time delay. As well as, under this strategy and uniformly asymptotically stable function, by combining trajectory based approach and improved Razumikhin method, mean square exponential stability criterion of impulsive stochastic time-varying neural network with time delay is established. Finally, to demonstrate the viability of our theoretical findings, some instances are provided.

Automated summary

This paper investigates the impact of impulse on the stability of neural network and proposes a new strategy, namely impulsive density. By constructing Lyapunov function, sufficient conditions for mean square asymptotical stability of impulsive stochastic time-varying neural network without time delay are established based on this strategy. Furthermore, under this strategy and uniformly asymptotically stable function, a mean square exponential stability criterion for impulsive stochastic time-varying neural network with time delay is established by combining trajectory based approach and improved Razumikhin method. Finally, some instances are provided to demonstrate the viability of the theoretical findings.