An approach to fuzzy state tracking control for chaotic synchronization in secure communication

This paper presents a fuzzy state tracking control scheme for chaotic synchronized secure communication based on the T-S fuzzy model of chaos. The conditions for dealing with the stability of the overall synchronization error system are proved by utilizing Lyapunov Stability Theory, and formulated into linear matrix inequalities (LMIs) afterwards. The structure of the controller is simply linear without observer. The methodology is applied to the well-known continuous-time Lorenz system, which has verified the validity of our theoretical derivations. The synchronization error is zero, and the synchronization settle time is 3.47s, only 16.5% of the one in literature [6] under the same simulation circumstances. It could be applied to discrete-time chaotic systems without difficulty. The numerical simulation of secure communication for double period wave and speech signal also has been implemented with expected results.