Center for Global Converging Humanities, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin 17104, Republic of Korea.
School of Electrical Engineering, Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju 28644, Republic of Korea.
Neural Netw. 2018 Oct;106:67-78. doi: 10.1016/j.neunet.2018.06.010. Epub 2018 Jun 21.
This paper is concerned with the problem of passivity for uncertain neural networks with time-varying delays. First, the recently developed integral inequality called generalized free-matrix-based integral inequality is extended to estimate further tight lower bound of integral terms. By constructing a suitable augmented LKF, an enhanced passivity condition for the concerned network is derived in terms of linear matrix inequalities (LMIs). Here, the integral terms having three states in its quadratic form is estimated by the proposed Lemma. As special cases of main results, for neural networks without uncertainties, passivity and stability conditions are derived. Through three numerical examples, it will be shown that the developed conditions can promote the level of passivity and stability criteria.
本文研究了具有时变时滞的不确定神经网络的被动性问题。首先，将最近提出的广义自由矩阵积分不等式扩展到进一步估计积分项的紧下界。通过构造一个合适的增广 LKF，基于线性矩阵不等式（LMI）推导出了所关注网络的增强被动性条件。这里，通过所提出的引理来估计二次形式中具有三个状态的积分项。作为主要结果的特例，对于没有不确定性的神经网络，推导出了被动性和稳定性条件。通过三个数值例子，将表明所提出的条件可以提高被动性和稳定性标准的水平。
