Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays
Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays
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DOI：
10.1109/tnnls.2018.2797279
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发表时间：
2018-02
影响因子：
10.4
通讯作者：
Xianming Zhang;Q. Han;Jun Wang
中科院分区：
文献类型：
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作者：
Xianming Zhang;Q. Han;Jun Wang
研究了一类具有时变时滞的神经网络的全局渐近稳定性，其中时滞函数是可微的一致有界的，时滞导数从上面有界。首先，通过引入一些具有柔性维度的松弛向量，给出了一个一般的互反凸不等式。这个不等式以凸组合的形式提供了一个比现有的一些组合更紧密的界限。其次，通过构造适当的Lyapunov-Krasovskii泛函，在时滞导数的下界已知的情况下，分析了两类时变时滞神经网络的全局渐近稳定性。第三，注意到一些Lyapunov-Krasovskii泛函的导数估计的稳定性的充分条件是时滞函数及其导数上的仿射的，允许时滞集可以被细化以给出所研究的神经网络的较不保守的稳定性判据。最后，给出了两个数值算例，验证了该方法的有效性。
This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov–Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov–Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method.