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

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）