基于Wirtinger积分不等式的时滞不确定神经网络无缘算法  

Passivity algorithm of uncertain neural networks with delay based on Wirtinger integral inequalities

作　　者：张芬[1,2] 张艳邦[1] 

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,陕西西安710071

出　　处：《西北师范大学学报（自然科学版）》2017年第5期12-18,共7页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61501388;11501482);咸阳师范学院青蓝人才项目(XSYQL201605)

摘　　要：基于Lyapunov稳定性理论,研究了一类含有不确定性的时滞神经网络的鲁棒无缘问题.首先构造含有三重积分项的Lyapunov-Krasovskii(LK)泛函,接着运用一阶和二阶Wirtinger积分不等式来估计LK泛函微分,得到了改善的时滞依赖的无缘条件,这些条件以线性矩阵不等式(LMIs)形式表出.最后,当时滞微分上界分别为0.9和1时,应用折半搜索算法获得了确保不确定时滞神经网络无缘的最大允许时滞上界.运用相对差将所得结果与最新文献结果相比,改善率分别提高了166%和103%,表明文中方法优于现有方法并且有较弱的保守性.另外,当时滞微分上界为0.9时,随机选取10个状态初始向量,利用MATLAB提供的Simulink平台进行系统状态响应曲线的仿真,结果支持所提方法的正确性和有效性.Based on Lyapunov stability theory,robust passivity problem for a class of uncertain neural networks with delay is studied in this paper.Firstly,a Lyapunov-Krasovskii（LK） functional containing a triple integral term is constructed.Next,the improved delay-dependent passivity conditions are derived,which are formulated in terms of linear matrix inequalities（LMIs） by using first-and second-order Wirtinger integral inequalities to estimate the derivative of the LK functional.Finally,when the upper bounds of delayed derivative are 0.9 and 1 respectively,the maximum allowable upper bounds of the delays are obtained to ensure the passivity of uncertain neural network with delay via binary search algorithm.Moreover,the comparison results on the allowable delay bounds obtained by employing the results in the current paper and ours in this paper are given by the use of relative difference,the improvement over the current best result is over 166% for 0.9,and over 103% for 1,which show that the proposed method is superior to the existing methods and less conservatism.In addition,when the upper bound of delayed derivative is 0.9,system state response curves are given with 10 randomly initial state vectors selected in virtue of MATLAB Simulink platform,which shows the correctness and effectiveness of the proposed method.

关 键 词：Wirtinger积分不等式 时滞神经网络 不确定 无缘 线性矩阵不等式 

分 类 号：O175.13[理学—数学]