Abstract
In this paper, the pth moment exponential stability for a class of impulsive delayed Hopfield neural networks is investigated. Some concise algebraic criteria are provided by a new method concerned with impulsive integral inequalities. Our discussion neither requires a complicated Lyapunov function nor the differentiability of the delay function. In addition, we also summarize a new result on the exponential stability of a class of impulsive integral inequalities. Finally, one example is given to illustrate the effectiveness of the obtained results.
Highlights
In the past few years, the artificial neural networks introduced by Hopfield [1, 2] have become a significant research topic due to their wide applications in various areas such as signal and image processing, associative memory, combinatorial optimization, pattern classification, etc. [3,4,5]
Since time delays are frequently encountered for the finite switching speed of neurons and amplify in implementation of neural networks, it is meaningful to discuss the effect of time delays on the stability of Hopfield neural networks (HNNs)
Ren et al [19] considered the mean-square exponential inputto-state stability for a class of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion by constructing an appropriate G-Lyapunov–Krasovskii functional, mathematical induction approach, and some inequality techniques
Summary
In the past few years, the artificial neural networks introduced by Hopfield [1, 2] have become a significant research topic due to their wide applications in various areas such as signal and image processing, associative memory, combinatorial optimization, pattern classification, etc. [3,4,5]. Among the existing stability results of impulsive delayed systems, one powerful technique is Lyapunov method Ren et al [19] considered the mean-square exponential inputto-state stability for a class of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion by constructing an appropriate G-Lyapunov–Krasovskii functional, mathematical induction approach, and some inequality techniques.
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