一类复值神经网络的随机指数鲁棒稳定性  

Stochastic Exponential Robust Stability of a Class of Complex-Valued Neural Networks

作　　者：徐晓惠[1] 施继忠[2] 严超 张继业[3] 徐延海[1] XU Xiao-hui;SHI Ji-zhong;YAN Chao;ZHANG Ji-ye;XU Yan-hai(Key Laboratory of Automobile Measurement and Control & Safety,Xihua University Chengdu 610039;College of Engineering,Zhejiang Normal University Jinhua Zhejiang 321004;National Traction Power Laboratory,Southwest Jiaotong University Chengdu 610031)

机构地区：[1]西华大学汽车测控与安全四川省重点实验室,成都610039 [2]浙江师范大学工学院,浙江金华321004 [3]西南交通大学牵引动力国家重点实验室,成都610031

出　　处：《电子科技大学学报》2019年第3期374-380,共7页Journal of University of Electronic Science and Technology of China

基　　金：四川省教育厅自然科学重点项目(17ZA0364);国家自然科学基金(51775448;11402214;11572264);四川省重点实验室研究基金(szjj2017-074);教育部重点实验室研究基金(szjj2016-007)

摘　　要：为分析Markova跳变参数对系统的影响,研究了一类具有Markova跳变参数和变时滞的复数域区间神经网络的动态行为。在假定复数域激活函数仅满足Lipchitz条件的情况下,首先利用M矩阵理论和同胚映射相关原理,研究了该系统平衡点的存在性和唯一性。然后利用矢量Lyapunov函数法分析了不同模式下平衡点的随机指数鲁棒稳定性。建立的稳定性条件推广了现有结论,并且容易验证。最后,通过一个数值仿真算例验证了所得结论的可行性。In order to analyze the influence of the Markova jumping parameters on the system, this paper deals with dynamic behavior analysis for a class of interval neural networks defined in complex number domain with Markova jumping parameters and time-varying delays. It is assumed that the activation functions defined in complex number domain satisfy Lipschitz condition. Firstly, the existence and uniqueness of the equilibrium point of the addressed system are studied by employing the M-matrix theory and the homeomorphism mapping theory. Then, the stochastic exponential robust stability of the equilibrium point is analyzed based on the idea of the vector Lyapunov function method. The presented stability analysis is the generalization of existing ones not only, but also easy to be verified in the practice applications. Finally, a numerical example with several simulation results is given to illustrate the feasibility of the obtained results in this paper.

关 键 词：复数域 Markova跳变参数 神经网络 随机指数鲁棒稳定性 变时滞 矢量Lyapunov函数法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]