This article addresses the synchronization issue for inertial neural networks (INNs) with heterogeneous time-varying delays and unbounded distributed delays, in which the state quantization is considered. First, by fully considering the delay and sampling time point information, a modified looped-functional is proposed for the synchronization error system. Compared with the existing Lyapunov-Krasovskii functional (LKF), the proposed functional contains the sawtooth structure term V8(t) and the time-varying terms ex(t-βħ(t)) and ey(t-βħ(t)) . Then, the obtained constraints may be further relaxed. Based on the functional and integral inequality, less conservative synchronization criteria are derived as the basis of controller design. In addition, the required quantized sampled-data controller is proposed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness and superiority of the proposed scheme in this article.

中文翻译：

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提交给基于可解释表示学习的复杂系统智能检查和维护的特刊：通过采样数据控制实现无限延迟的惯性神经网络同步。

本文解决了具有异构时变延迟和无界分布式延迟的惯性神经网络 (INN) 的同步问题，其中考虑了状态量化。首先，通过充分考虑延迟和采样时间点信息，为同步误差系统提出了改进的循环泛函。与现有的 Lyapunov-Krasovskii 泛函 (LKF) 相比，所提出的泛函包含锯齿结构项 V8(t) 和时变项 ex(t-βħ(t)) 和 ey(t-βħ(t)) 。然后，可以进一步放宽获得的约束。基于功能和积分不等式，不太保守的同步准则被推导出作为控制器设计的基础。此外，通过求解一组线性矩阵不等式，提出了所需的量化采样数据控制器。最后给出了两个数值例子来说明本文所提方案的有效性和优越性。