Practical fixed-time Lyapunov criterion of stochastic nonlinear systems and its application

This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equation theory and Lyapunov functional method. Building on this foundation, several specific judgment forms of the PFxT-SP are established and corresponding estimates for the settling times (ST) are obtained. Compared to general FxT-SP, PFxT-SP requires the system converge to a specific region within ST T, where the region and ST can be determined based on the system parameters, and they are independent of the initial values. Additionally, a unified practical fixed-time stability (PFxT-S) criterion of deterministic systems and two specific judgments are presented. Furthermore, the PFxT synchronization of T-S fuzzy complex networks with and without diffusion term is investigated. Finally, the feasibility of the theoretical results are illustrated by some simulation examples.