Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay
Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay
复制标题
基于辅助函数的积分不等式方法对区间时变时滞神经网络的鲁棒无源性分析
DOI：
10.1016/j.neucom.2018.04.026
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发表时间：
2018
期刊：
影响因子：
6
通讯作者：
Zh iLi
中科院分区：
文献类型：
--
作者：
Fen Zhang;Zh iLi
本文研究了具有区间时变时滞的不确定神经网络的无源性问题。首先，构造一个包含两个三重积分项的增广Lyapunov-Krasovskii泛函（LKF），并利用一个基于辅助函数的积分不等式（AFBI）对LKF导数中的增广单重积分项进行处理.其次，将AFBI的一种特殊形式应用于处理三重积分时间导数中常被忽略的延迟积项。因此，不太保守的延迟依赖的无源性准则推导出正常的延迟神经网络（DNN）的线性矩阵不等式（LMI）的形式。此外，在相同的LKF下，对于不含延迟乘积型项的正常DNN，得到了延迟相关无源性准则。随后，这些标准扩展到DNN参数的不确定性。最后，四个数值例子和模拟来说明所提出的准则的有效性。
In this paper, we study the problem of passivity for uncertain neural networks with interval time-varying delay. Firstly, a suitable augmented Lyapunov–Krasovskii functional (LKF) containing two triple integral terms is constructed and an auxiliary function-based integral inequality (AFBI) is used to manipulate the augmented single integral terms in the derivative of LKF. Secondly, a special form of the AFBI is applied to deal with the delay-product-type term, which was used to be ignored in the time derivative of a triple integral term. As a result, less conservative delay-dependent passivity criteria are derived for normal delayed neural networks (DNNs) in the form of linear matrix inequalities (LMIs). In addition, with the same LKF, delay-dependent passivity criteria are obtained for normal DNNs without the delay-product-type term. Subsequently, these criteria are extended to DNNs with parameter uncertainties. Finally, four numerical examples and simulations are provided to illustrate the effectiveness of the proposed criteria.