一类区间时滞忆阻神经网络的稳定性控制  

Stability Control for a Type of Memristive Neural Network with Interval Time-varying Delay

作　　者：赵一飞 曹梦亭 褚佳奕 崔铠亭 章联生[2] ZHAO Yifei;CAO Mengting;CHU Jiayi;CUI Kaiting;ZHANG Liansheng(College of New Materials and Chemical Engineering,Beijing Institute of Petrochemical Technology,Beijing 102617,China;Dept.of Math and Phy,Beijing Institute of Petrochemical Technology,Beijing 102617,China)

机构地区：[1]北京石油化工学院新材料与化工学院,北京102617 [2]北京石油化工学院数理系,北京102617

出　　处：《北京石油化工学院学报》2024年第2期60-68,共9页Journal of Beijing Institute of Petrochemical Technology

基　　金：2023年国家级大学生创新创业计划项目(2023J00120)。

摘　　要：鉴于忆阻神经网络(memristive neural network,MNN)的数学模型是一种右端不连续的微分方程,经典的微分方程理论不再适用。借助微分包含理论和Filippov解的框架,将这一神经网络系统转化为通常的神经网络系统,并建立了时滞一次函数形式的新型李雅普诺夫-克拉索夫斯基泛函(Lyapunov-Krasovskii functional,LKF),运用积分不等式和倒数凸组合不等式估计其导数,得到了该系统渐近稳定的充分条件并以线性矩阵不等式(linear matrix inequalities,LMIs)形式给出,便于用MATLAB软件验证。数值仿真结果表明,所得到结论正确且可实现。This paper is concerned with the stability problem for a kind of memristive neural network(MNN)with interval time-varying delays.Since the model of the MNN is a differential equation with a discontinuous function on right hand side,the classical theory of differential equations is beyond appliance.By means of the theory of differential inclusion and the framework of Filippov solution,the delayed MNN can be transformed into some common delayed neural network and a novel Lyapunov-Krasovskii functional(LKF)is constructed with a first-order function regarding time delay.Utilizing some integral inequalities and the reciprocally convex combination inequality to assess its time derivative,we obtain a sufficient condition guaranteeing the asymptotic stability of the delayed MNN in the form of linear matrix inequalities(LMIs),which can be checked easily by MATLAB.Ultimately,it is shown through numerical example that the proposed method is valid and realizable.

关 键 词：忆阻神经网络 全局渐进稳定 时变时滞 线性矩阵不等式 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]