LMI-based fuzzy chaotic synchronization and communications

This paper addresses synthesis approaches for signal synchronization and se cure communications of chaotic systems by using fuzzy system design methods based on linear matrix inequalities (LMIs). By introducing a fuzzy modelin g methodology, many well-known continuous and discrete chaotic systems can be exactly represented by Takagi-Sugeno (T-S) fuzzy models with only one pr emise variable. Following the general form of fuzzy chaotic models, the str ucture of the response system is first proposed. Then, according to the app lications on synchronization for the fuzzy models that have common bias ter ms or the same premise variable of drive and response systems, the driving signals are developed with four different types: fuzzy, character, crisp, a nd predictive driving signals. Synthesizing from the observer and controlle r points of view, all types of drive-response systems achieve asymptotic sy nchronization. For chaotic communications, the asymptotical recovering of m essages is ensured by the same framework. It is found that many well-known chaotic systems can achieve their applications on asymptotical synchronizat ion and recovering messages in secure communication by using either one typ e of driving signals or all. Several numerical simulations are shown with e xpected satisfactory performance.