Fixed/prescribed-time synchronization of state-dependent switching neural networks with stochastic disturbance and impulsive effects.

Abstract

This paper investigates the fixed-time synchronization (FXTS) and prescribed-time synchronization (PSTS) problems of state-dependent switching neural networks (SDSNNs) with stochastic disturbances and impulsive effects. By leveraging the average impulsive interval, comparison principle, and interval matrix methodology, this study advances a novel analytical framework. Departing from conventional approaches, we reformulate stochastic disturbed and impulsive SDSNNs as interval-parameter systems through rigorous interval matrix transformation. Consequently, we derive some sufficient conditions in the form of linear matrix inequalities (LMIs) to ensure the realization of FXTS and PSTS. Since impulsive effects can potentially compromise synchronization stability, careful controller design becomes critical. To address this challenge, we develop a unified proportional integral (PI) control framework. Through proper adjustment of its control parameters, this framework enables the system to achieve both FXTS and PSTS. Moreover, by reasonably configuring the relationship between the impulsive intensity and the prescribed time, the synchronization performance can be balanced. Finally, we demonstrate the effectiveness of the theoretical results through two examples.