Adaptive fuzzy control design for synchronization of chaotic time-delay system

This paper focuses on an adaptive synchronization for a class of uncertain chaotic systems (CSs) with time delay. The chaotic systems are represented by Takagi–Sugeno (T-S) fuzzy model. In order to estimate the unknown parameters of the uncertain chaotic systems, we use advanced adaptive laws with smooth projection operator to solve it. In addition, we take the adaptive law as a part of Lyapunov function to make the chaotic systems stable. Different from the previous study of adaptive synchronization of uncertain chaotic systems, this paper fully considers the effect of time delay on uncertain chaotic systems. Finally, by constructing a suitable Lyapunov function (LKF) and using linear matrix inequality (LMI) theory, we can obtain the stability condition of closed-loop system. Furthermore, the simulation cases in this paper illustrate the robust performance of the error system is guaranteed under the uncertain dynamic equation modeling.