Robust Control and Synchronization of Fractional-Order Unified Chaotic Systems

Abstract

This work examines the understanding and regulation of chaotic systems via fractal system dynamics. The criteria for the asymptotic stability of the equilibrium point are examined. This signifies that the point is stable and demonstrates local attraction, which is essential for the system’s behavior over time. The independent uncertainty in the system, denoted by αj, may vary over time but is constrained by a constant δ > 0. This factor is crucial for comprehending the system’s responsiveness to varying environments. The system’s stability is further analyzed through the negative semi-definiteness of the fractional derivative of the Lyapunov function, indicating that the system’s origin stays stable given specific beginning circumstances. The study presents a thorough framework for analyzing and controlling chaotic systems using fractal system dynamics, emphasizing stability and the impact of uncertainty.