T-S fuzzy modeling and asymptotic synchronization of two nonidentical discrete-time hyperchaotic maps

Chaotic synchronization is the key technique in secure communication systems. This paper proposes a novel control method to synchronize two nonidentical discrete-time hyperchaotic maps based on T-S fuzzy models. Firstly, a universal fuzzy modeling process is presented for most discrete-time hyperchaotic maps. Then, a simple fuzzy controller is designed based on the PDC technique. The asymptotic stability criteria of the fuzzy synchronization error system is derived by applying linear system theory. Finally, simulation results are given to demonstrate the effectiveness of the proposed fuzzy synchronization scheme for two nonidentical discrete-time hyperchaotic maps. Because a linear closed-loop synchronous error system can be obtained by the proposed fuzzy synchronous controller design method in this paper, many satisfactory performance indices can be achieved, such as rapid response and short transient time, etc.