This article is dedicated to designing distributed state estimators for time-varying delay systems. The filtering network communication topology is time-varying, and it is presumed that the switching mechanism follows a homogeneous Markov chain, with partially unknown information in the probability transition matrix. An adaptive event-triggered mechanism is embedded in the sensor network, which reduces unnecessary communication data and saves communication resources. By utilising the mode-dependent Lyapunov function, sufficient conditions are deduced to ensure the $H_{\infty }$-consensus performance for the filtering error dynamics. Then, some intensive analysis is performed to obtain the explicit expressions of the distributed $H_{\infty }$ state estimator by introducing slack variables and free-connection weighting matrices. Finally, two numerical simulations are proposed to demonstrate the effectiveness of theoretical results.

本文致力于为时变延迟系统设计分布式状态估计器。滤波网络通信拓扑是时变的，假设切换机制遵循齐次马尔可夫链，概率转移矩阵中的信息部分未知。传感器网络中嵌入了自适应事件触发机制，减少了不必要的通信数据，节省了通信资源。利用依赖于模态的 Lyapunov 函数，推导出充分条件以确保$H_{\infty }$- 过滤误差动态的共识性能。然后，进行一些深入的分析以获得分布式的显式表达式$H_{\infty }$通过引入松弛变量和自由连接加权矩阵来估计状态。最后，提出了两个数值模拟来证明理论结果的有效性。