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Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay

机译：区间时变时滞神经网络鲁棒无源分析的基于辅助函数的积分不等式方法

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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-producttype 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. (C) 2018 Published by Elsevier B.V.
机译：在本文中，我们研究了具有时变间隔的不确定神经网络的无源性问题。首先，构造了包含两个三重积分项的合适的增广Lyapunov-Krasovskii泛函（LKF），并使用基于辅助函数的积分不等式（AFBI）来操纵LKF导数中的增广单积分项。其次，采用AFBI的一种特殊形式来处理延迟乘积类型项，该项在三重积分项的时间导数中被忽略。结果，以线性矩阵不等式（LMI）的形式为正常延迟神经网络（DNN）导出了较不保守的依赖于延迟的无源标准。此外，使用相同的LKF，可以获得没有延迟乘积类型项的正常DNN的延迟依赖无源标准。随后，这些标准扩展到具有参数不确定性的DNN。最后，提供了四个数值示例和仿真来说明所提出标准的有效性。 （C）2018由Elsevier B.V.发布

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