This paper deals with the problem of the fault-tolerant fuzzy master–slave systems synchronization through an adaptive event-triggered scheme (AETS). First, a Takagi–Sugeno (T–S) fuzzy model is employed to represent the master–slave system dynamics. Second, an AETS is introduced to judge whether the newly sampled controller’s signals should be released to the slave system or not. Consequently, the less computation resources and network bandwidth are utilized under the AETS. Meanwhile, a novel adaptive law is designed to achieve the threshold of event-triggering condition on-line. Third, a novel fuzzy controller is designed, containing a state feedback controller and a fault compensator to achieve the fault-tolerant synchronization, which is formulated to study the global asymptotical stability of the error system. As a results, applying Lyapunov theory and inequality technique, new sufficient condition is obtained to guarantee the stability of the error system. Further, the controller gain and the weight of event-triggering condition are designed through linear matrix inequalities (LMIs) approach. Finally, a numerical simulation example is employed to demonstrate the practical utility of this method.

中文翻译：

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基于自适应事件触发方案的模糊采样控制器混沌系统的容错同步

本文通过自适应事件触发方案（AETS）解决了容错模糊主从系统的同步问题。首先，采用Takagi-Sugeno（TS）模糊模型来表示主从系统动力学。其次，引入AETS来判断是否应将新采样的控制器的信号释放到从属系统。因此，在AETS下使用较少的计算资源和网络带宽。同时，设计了一种新颖的自适应律，以在线达到事件触发条件的阈值。第三，设计了一种新型的模糊控制器，该控制器包含一个状态反馈控制器和一个故障补偿器，以实现容错同步，从而研究了误差系统的全局渐近稳定性。结果，应用李雅普诺夫理论和不等式技术，获得了新的充分条件，以保证误差系统的稳定性。此外，控制器增益和事件触发条件的权重是通过线性矩阵不等式（LMI）方法设计的。最后，通过一个数值仿真例子来说明该方法的实用性。