Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems

This paper presents synthesis approaches for synchronization and secure com munications of chaotic systems by using fuzzy model-based design methods. M any well-known continuous and discrete chaotic systems can be exactly repre sented by TS fuzzy models with only one premise variable. According to the applications on synchronization and signal modulation, the general fuzzy mo dels may have either i) common bias terms; or ii) the same premise variable and driving signal. Then we propose two types of driving signals, namely, fuzzy driving signal and crisp driving signal, to deal with the asymptotica l synchronization and secure communication problems for cases i! and ii), r espectively, Based on these driving signals, the solutions are found by sol ving LMI problems. It is worthy to note that many well-known chaotic system s, such as Duffing system, Chua's circuit, Rossler's system, Lorenz system, Henon map, and Lozi map can achieve their applications on asymptotical syn chronization and recovering messages in secure communication by using eithe r the fuzzy driving signal or the crisp driving signal. Finally, several nu merical simulations are shown to verify the results.