Mean-square exponential input-to-state stability of stochastic delayed neural networks

In this paper, we focus on the stability problem for a class of stochastic delayed recurrent neural networks. Different from the traditional stability criteria, we introduce and study a new stability criterion: the mean-square exponential input-to-state stability. To the best of our knowledge, this new stability criterion has never been discussed in the field of stochastic recurrent neural networks. The main objective of the paper is to fill the gap. With the help of the Lyapunov-Krasovskii functional, stochastic analysis theory and Itô's formula, we prove that the addressed system is mean-square exponentially input-to-state stable. Moreover, two numerical examples and their simulations are presented to verify the theoretical results well.