This article investigates the event-triggered synchronization of delayed neural networks (NNs). A novel integral-based event-triggered scheme (IETS) is proposed where the integral of the system states, and past triggered data over a period of time are used. With the proposed IETS, the integral event-triggered synchronization problem becomes a distributed delay problem. Using the Bessel-Legendre inequalities, sufficient conditions for the existence of a controller that ensures asymptotic synchronization are provided in the form of linear matrix inequalities (LMIs). Illustrative examples are used to demonstrate the advantages of the proposed IETS method over other event-triggered scheme (ETS) methods. Moreover, this IETS method is applied to the image encryption and decryption. A novel encryption algorithm is proposed to enhance the quality of the encryption process.

中文翻译：

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通过基于积分的事件触发方案对延迟神经网络进行同步。

本文研究了延迟神经网络（NN）的事件触发同步。提出了一种新颖的基于积分的事件触发方案（IETS），其中使用了系统状态的积分以及一段时间内的过去触发数据。利用提出的IETS，积分事件触发的同步问题变成了分布式延迟问题。使用Bessel-Legendre不等式，以线性矩阵不等式（LMI）的形式为确保渐近同步的控制器的存在提供了充分的条件。说明性示例用于证明所提出的IETS方法相对于其他事件触发方案（ETS）方法的优势。而且，该IETS方法被应用于图像加密和解密。