In this paper, the $H_{\infty }$ state estimation problem is studied for a class of multi-rate artificial neural networks with integral measurements. A novel method, rather than the widely used lifting technique, is proposed to transform the multi-rate artificial neural networks to single-rate switched ones. The purpose of the addressed $H_{\infty }$ state estimation problem is to design an estimator such that the estimation error dynamics is exponentially stable and the $H_{\infty }$ performance requirement is satisfied. First, with the help of the Lyapunov–Krasovskii functional and the switched system approach, sufficient conditions are derived under which the existence of the desired estimator is ensured. Then, the characterization of the estimator gains is realized by solving certain linear matrix inequalities. Finally, two illustrative examples are given that confirm the usefulness of the developed $H_{\infty }$ state estimation scheme and reveal the influence of the multi-rate sampling on the state estimation performance.

在本文中， $H_{\infty }$研究了一类带有积分测量的多速率人工神经网络的状态估计问题。提出了一种新的方法，而不是广泛使用的提升技术，将多速率人工神经网络转换为单速率交换神经网络。解决的目的$H_{\infty }$ 状态估计问题是设计一个估计器，使得估计误差动态指数稳定，并且 $H_{\infty }$性能要求得到满足。首先，借助Lyapunov–Krasovskii泛函和交换系统方法，可以推导出充分的条件，以确保所需估计量的存在。然后，通过求解某些线性矩阵不等式来实现估计器增益的表征。最后，给出了两个说明性的例子，证实了所开发工具的有效性。$H_{\infty }$ 状态估计方案，揭示多速率采样对状态估计性能的影响。