Abstract: Based on probability theory and the Lyapunov stability theory, the stability problem for a class of neural networks with probabilistic time-varying delay is studied. By constructing a proper Lyapunov-Krasovskii functional（KLF）, and using Wirtinger-based inequality and the reciprocal convex technique to estimate the upper of the time derivative of the KLF, a novel sufficient criterion is derived to guarantee neural networks with time-varying delay to be asymptotically stable in the mean-square sense. The criterion formulated in terms of LMIs（Linear Matrix Inequalities） is dependent not only on the upper bound of the time delay but also on time delay’s probability distribution. Finally, two numerical examples are given to illustrate that the approach proposed in this paper is more effective and less conservative than some existing ones.

Key words: delayed neural networks, probabilistic time-varying delay, asymptotical stability, reciprocal convex technique, Linear Matrix Inequalities（LMIs）

摘要： 基于概率理论和Lyapunov稳定性理论，研究一类具有概率分布时滞神经网络稳定性问题。通过构造合适的Lyapunov-Krasovskii（LK）泛函，运用Wirtinger不等式和倒凸技术来估计LK泛函导数的上界，得到了确保该类时滞神经网络在均方意义下的全局渐近稳定的新判据。该判据以LMIs形式表出，它不但依赖于时滞的上界，而且依赖于时滞的概率分布。给出两个数值例子，仿真表明所提方法的有效性和较弱的保守性。

关键词: 时滞神经网络, 概率时滞, 渐近稳定, 倒凸技术, 线性矩阵不等式