Zuo Zhiqiang, Yang Cuili, Wang Yijing
Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin, China.
IEEE Trans Neural Netw. 2010 Feb;21(2):339-44. doi: 10.1109/TNN.2009.2037893. Epub 2009 Dec 18.
This brief deals with the problem of stability analysis for a class of recurrent neural networks (RNNs) with a time-varying delay in a range. Both delay-independent and delay-dependent conditions are derived. For the former, an augmented Lyapunov functional is constructed and the derivative of the state is retained. Since the obtained criterion realizes the decoupling of the Lyapunov function matrix and the coefficient matrix of the neural networks, it can be easily extended to handle neural networks with polytopic uncertainties. For the latter, a new type of delay-range-dependent condition is proposed using the free-weighting matrix technique to obtain a tighter upper bound on the derivative of the Lyapunov-Krasovskii functional. Two examples are given to illustrate the effectiveness and the reduced conservatism of the proposed results.
本文研究了一类时变延迟在一定范围内的递归神经网络（RNN）的稳定性分析问题。推导了与延迟无关和与延迟相关的条件。对于前者，构造了一个增广Lyapunov泛函并保留了状态导数。由于所得到的准则实现了Lyapunov函数矩阵与神经网络系数矩阵的解耦，因此可以很容易地扩展到处理具有多面体不确定性的神经网络。对于后者，提出了一种新型的依赖延迟范围的条件，利用自由加权矩阵技术在Lyapunov-Krasovskii泛函导数上获得更紧的上界。给出了两个例子来说明所提结果的有效性和降低的保守性。
