Control and Stabilization of Chaotic Systems Using Lyapunov Stability Theory

This paper proposes the application of Lyapunov stability theory for controlling and stabilizing chaotic systems. The system's chaotic behavior is mastered through a suitable Lyapunov function and control law, leading to rapid convergence toward a stable equilibrium. The study also investigates the effects of time-delayed control law on system stabilization. The numerical simulations validated the proposed approach and showed its efficiency to control, successfully, the system's chaotic behavior, and its potential for practical applications in various chaotic systems.