一类带有混合时滞的神经网络全局渐进稳定分析  

Global Asymptotic Stability of Generalized Neural Networks with Infinite Distributed Delays

作　　者：宫大为[1] 王占山[1] 黄博南[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110819

出　　处：《东北大学学报（自然科学版）》2011年第6期773-776,785,共5页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(50977008;61074073;61034005);国家高技术研究发展计划项目(2009AA04Z127)

摘　　要：针对一类具有离散和无穷分布时滞的神经网络模型,通过构造新的Lyapunov函数,解决了含有无穷分布时滞的系统稳定问题,给出了全局渐近稳定的充分条件.首次以Hadamard乘积将系统用向量形式表示,并用线性矩阵不等式表示所得结果,稳定判据不依赖于时间延迟大小,不要求神经元激励函数的有界性、可微性,只与连接矩阵和延迟的导数项有关,易于用MATLAB工具箱LMI进行求解.最后,通过仿真例子与其他文献中的结果作了比较,证明了理论的有效性.This paper investigates the global asymptotic stability of the neural networks with discrete and infinite distributed delays.Without assuming the boundedness and differentiability of neuron activation function,a new criteria is proposed by way of constructing a suitable Lyapunov function.Using Hadamard product,a vector-matrix form of neural networks with infinite distributed delays is obtained.It solves the problem with infinite distributed delays only by imposing constraints on the interconnected matrices and derivative of time delays.The condition is expressed by a linear matrix inequality,which can be easily computed in MATLAB toolbox.Comparisons between the results and the existing ones through two numerical examples imply the effectiveness of the proposed result.

关 键 词：神经网络 无穷分布时滞 渐近稳定 线形矩阵不等式(LMI) LYAPUNOV函数 

分 类 号：TG335.58[金属学及工艺—金属压力加工]