Controlling fractional-order new chaotic system based on Lyapunov equation

Abstract

A new circuit unit for the analysis and synthesis of the chaotic behaviors in the new fractional-order system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to demonstrate the dynamic behaviors of the fractional-order Liu system with α=09 An effective controller is designed based on a theory of stability identification based on Lyapunov equation. The results between simulation and experiment are in good agreement, thereby proving the existence of chaos in the fractional-order new system and the effectiveness of our proposed control method.