Fixed-time Control and Synchronization of Chaotic Systems Based on Impulsive Control

Abstract This study focuses on fixed-time stability and synchronization challenges in chaotic systems using impulsive control techniques. A ground breaking fixed-time stability theorem with optimal convergence time is introduced, merging impulsive and fixed-time control strategies. This approach establishes fixed-time stability criteria for chaotic system control and synchronization. Unlike continuous controllers in the existing literature, the proposed impulsive control method achieves system stability and synchronization within a fixed time, offers flexible impulsive sequences tailored to practical needs, reduces control energy consumption, and enhances practicality. Numerical simulations demonstrate the effectiveness and feasibility of the proposed methodology.