An Improved Fixed-Time Stability Theorem and its Application to the Synchronization of Stochastic Impulsive Neural Networks

Qingjie Wang, Hui Zhao, Aidi Liu, Sijie Niu, Xizhan Gao, Xiju Zong, Lixiang Li

Abstract: In this paper, the fixed-time synchronization of stochastic impulsive neural networks with time-varying delays is studied. For the stability problem of nonlinear systems with impulsive effects, a new fixed-time stability theorem is proposed. Compared with other fixed-time stability theorems, it has better generality. Then, in order to realize fixed-time synchronization, a state feedback controller and an adaptive controller are designed respectively. Moreover, based on the new theorem, sufficient conditions for fixed-time synchronization of stochastic impulsive neural networks with time-varying delays are given. Finally, two simulation examples are given to verify the effectiveness of the theoretical results.