Li Hongyi, Chen Bing, Zhou Qi, Qian Weiyi
Institute of Complexity Science, Qingdao University, Qingdao 266071, China.
IEEE Trans Syst Man Cybern B Cybern. 2009 Feb;39(1):94-102. doi: 10.1109/TSMCB.2008.2002812.
This paper is concerned with the problem of the robust stability of nonlinear delayed Hopfield neural networks (HNNs) with Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed HNNs are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping HNNs with interval delays. Time delays here are assumed to be time-varying and belong to the given intervals. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality approach, stability conditions are proposed in terms of the upper and lower bounds of the delays. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.
本文研究了具有马尔可夫跳跃参数的非线性时滞霍普菲尔德神经网络（HNNs）基于Takagi-Sugeno（T-S）模糊模型的鲁棒稳定性问题。首先，将非线性时滞HNNs建立为一种改进的T-S模糊模型，其中后件部分由一组具有区间时滞的马尔可夫跳跃HNNs组成。这里假设时滞是时变的且属于给定区间。基于Lyapunov-Krasovskii稳定性理论和线性矩阵不等式方法，根据时滞的上下界提出了稳定性条件。最后，通过数值例子说明了所提方法的有效性。
