Stability and Synchronization of Set-Valued Saturated Impulsive Nonlinear System

This paper investigates the criteria for the local exponential stability and synchronization of the set-valued saturated impulsive nonlinear system. Initially, the saturation nonlinearity of the system is addressed through the sector nonlinear model approach and the polyhedral representation approach, and the sufficient condition for the local exponential stability is derived by combining the generalized Cauchy-Schwarz inequality and the average impulsive interval method. Subsequently, by designing a saturated impulsive controller, the sufficient condition for the synchronization of the drive-response system is established, and the schematic diagram of the saturated impulsive input control is briefly plotted. Ultimately, the application example of the chaotic financial system is provided, and numerical simulations are conducted to verify the effectiveness of the theoretical results.