In this paper, we derive a new fixed-time stability theorem based on definite integral, variable substitution and some inequality techniques. The fixed-time stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, the fixed-time synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixed-time synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixed-time synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixed-time stability theorems. Moreover, the plaintext signals can be recovered according to the new fixed-time stability theorem, while the plaintext signals cannot be recovered according to the existing fixed-time stability theorems.

中文翻译：

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一个新的固定时间稳定性定理及其在神经网络固定时间同步中的应用。

在本文中，我们基于定积分，变量替换和一些不等式技术推导了一个新的固定时间稳定性定理。稳定时间的固定时间稳定性准则和上限估计公式与现有的固定时间稳定性定理不同。基于新的固定时间稳定性定理，通过设计反馈控制器研究神经网络的固定时间同步，并推导了充分的条件来保证神经网络的固定时间同步。为了显示所获得理论结果的可用性和优越性，我们提出了一种基于神经网络的固定时间同步的安全通信方案。数值模拟表明，新的建立时间上限估计公式比现有的固定时间稳定性定理中的公式更为严格。此外，可以根据新的固定时间稳定性定理来恢复明文信号，而不能根据现有的固定时间稳定性定理来恢复明文信号。