Synchronization and secure communication for chaotic systems: The modulated fuzzy system design

This paper presents a modulated T-S fuzzy model that can be applied to both continuous/discrete chaotic synchronization, chaotic model following and secure communication. The modulated T-S fuzzy model is constructed by choosing the common factor or the only variable of nonlinear terms in chaotic systems as the premise variable of fuzzy rules and output signal. Following this model, fuzzy chaotic synchronization is achieved by utilizing linear matrix inequalities design and some restricting conditions can be relaxed. This simplified design framework can be applied to many well-known chaotic systems. Also, for chaotic communications, this modulated T-S fuzzy model illustrates asymptotical recovering of the message. Moreover, the usage of combinational states as the coupling signal for Lure type systems is taken into consideration. In this case, the receiver design for synchronization and secure communication is also proposed. The simulation results are shown with expected satisfactory performance.