Stability of nonlinear systems with delayed saturated impulsive control and its application to synchronization of coupled neural networks with switching topology

Abstract

This study is presented on the local exponential stability (LES) of a class of nonlinear systems with discrete and distributed delays, using an impulsive control strategy that incorporates both input delays and actuator saturation. By integrating Lyapunov function theory, the Razumikhin techniques, the average impulsive interval (AII) method, and an improved convex hull representation method, several sufficient conditions for LES are established, with explicit estimates provided for the convergence rate and the region of attraction (ROA). Furthermore, within a unified framework for delayed saturated impulsive control (DSIC) analysis, a novel impulsive controller is designed to address the synchronization problem of coupled neural networks (CNNs) with switching topology and distributed-delay coupling. Criteria for local exponential synchronization are derived, along with an estimate of the ROA for the corresponding error system. On this basis, two optimization problems aimed at maximizing the ROA are formulated using convex optimization theory, addressing scenarios where the control parameters are either fixed or designable. Finally, the effectiveness of the proposed method is validated through two application examples accompanied by MATLAB numerical simulations.