Wang Zidong, Liu Yurong, Li Maozhen, Liu Xiaohui
IEEE Trans Neural Netw. 2006 May;17(3):814-20. doi: 10.1109/TNN.2006.872355.
In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.
在这封信中，考虑了一类具有混合时滞的随机Cohen-Grossberg神经网络的全局渐近稳定性分析问题，这类网络同时包含离散时滞和分布时滞。基于Lyapunov-Krasovskii泛函和随机稳定性分析理论，开发了一种线性矩阵不等式（LMI）方法，以推导几个充分条件，保证平衡点在均方意义下的全局渐近收敛。结果表明，如果两个LMI是可行的，那么所讨论的具有混合时滞的随机Cohen-Grossberg神经网络在均方意义下是全局渐近稳定的，其中LMI的可行性可以通过Matlab LMI工具箱轻松检验。还指出，主要结果包含一些现有结果作为特殊情况。给出了一个数值例子来证明所提出的全局稳定性准则的有用性。
