Generalized synchronization of chaotic systems with different orders by fuzzy logic constant controller

The fuzzy logic constant controller (FLCC) is introduced in this paper. Unlike traditional method, a simplest controller is proposed via fuzzy logic design and Lyapunov direct method. Controllers in traditional method by Lyapunov direct method are always complicated or the functions of errors. We propose a new idea to design constant numbers as controllers, while the constant numbers are decided by the upper bound and the lower bound of the error derivatives. Via fuzzy logic rules, the strength of controllers in our new approach can be adjusted according to the error derivatives. Consequently, the slave system becomes exactly and efficiently synchronized to the trajectory of master system through FLCC. Two examples, Lorenz system and four order Chen–Lee system, are presented to illustrate the effectiveness of the new controllers in chaos generalized synchronization.