This paper studies the adaptive event-based $H_{\infty }$ control problem for a class of T-S fuzzy distributed parameter system with parameter uncertain and actuator faults. To overcome the drawback of the period control scheme, an event-triggered control scheme with adaptive threshold is proposed to minimize the number of unnecessary sampled data transmission and to reduce the update frequency of the controller. Furthermore, a T-S fuzzy controller based on the adaptive event-triggered sampled data is designed to ensure the stochastic exponential stability of the distributed parameter system with $H_{\infty }$ disturbance attenuation performance. Based on a new Lyapunov functional and inequality technique, the stochastic exponential stability criterion of the closed-loop system is obtained, and the controller parameters are designed. The new developed inequality can reduce the conservatism of the stability criterion. Finally, the effectiveness of the theoretical calculation results is verified by numerical simulation, and the results are compared with the relevant literature in the simulation, showing that the methods and results in this paper are less conservative.

本文研究了基于自适应事件的$H_{\infty }$一类具有参数不确定和执行器故障的 TS 模糊分布参数系统的控制问题。为了克服周期控制方案的缺点，提出了一种具有自适应阈值的事件触发控制方案，以尽量减少不必要的采样数据传输次数并降低控制器的更新频率。此外，设计了一种基于自适应事件触发采样数据的TS模糊控制器，以确保分布式参数系统的随机指数稳定性$H_{\infty }$干扰衰减性能。基于新的Lyapunov泛函和不等式技术，得到了闭环系统的随机指数稳定性判据，并设计了控制器参数。新发展的不等式可以降低稳定性标准的保守性。最后通过数值模拟验证了理论计算结果的有效性，并在模拟中与相关文献进行了对比，表明本文方法和结果的保守性较小。