具有概率分布时滞的神经网络稳定性新判据  

New stability criteria for neural networks with probabilistic time-varying delay

作　　者：张芬[1,2] 张艳邦[1] ZHANG Fen;ZHANG Yanbang(College of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China;School of Mechano-Electronic Engineering, Xidian University, Xi’an 710071, China)

机构地区：[1]咸阳师范学院数学与信息科学学院,陕西咸阳712000 [2]西安电子科技大学机电工程学院,西安710071

出　　处：《计算机工程与应用》2016年第16期12-16,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.61501388;No.11501482);陕西省自然科学基金(No.2013JM1014);陕西省教育厅科学研究基金(No.14JK1797);咸阳师范学院高层次人才引进计划项目(No.14XSYK005);咸阳师范学院科研基金资助项目(No.13XSYK009)

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

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 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O175.13[自动化与计算机技术—控制科学与工程]