Finite-Time pth Moment Asymptotically Bounded for Stochastic Nonlinear Systems and Its Application in Neural Networks Synchronization

This article pays attention to finite-time (FnT) pth moment asymptotically bounded (MAB) for stochastic nonlinear systems (SNSs) and its application to pth moment quasi-synchronization (MQS) of stochastic neural networks (SNNs) based on parameter mismatches. First, this article develops FnT asymptotically bounded theorems SNSs. In detail, several new FnT pth MAB theorems of the SNSs are proposed, the mathematical expression of finite settlement time is obtained, and the bounds of MAB are estimated. Second, new sufficient conditions are designed to ensure FnT pth MQS of SNNs. In particular, novel FnT pth MQS conditions of the SNNs enlarge the value of p . Moreover, when the initial value of the system meets certain conditions, the smaller the $p$ is, the smaller the system synchronization control energy consumption is, which can be more meaningful. Finally, a numeric example illustrates the validity of the methods.