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.

本文着重于一类具有时滞的不确定混沌系统的自适应同步。混沌系统由Takagi-Sugeno（TS）模糊模型表示。为了估计不确定混沌系统的未知参数，我们使用带有平滑投影算子的高级自适应定律对其进行求解。此外，我们将自适应定律作为Lyapunov函数的一部分来使混沌系统稳定。与先前关于不确定混沌系统的自适应同步研究不同，本文充分考虑了时延对不确定混沌系统的影响。最后，通过构造一个合适的Lyapunov函数（LKF）并使用线性矩阵不等式（LMI）理论，我们可以获得闭环系统的稳定性条件。此外，