一类时滞神经网络的全局指数稳定性

利用M-矩阵和拓扑学等有关知识，通过构建向量李雅普诺夫函数，研究了一类包含分布时滞和可变时滞的神经网络的平衡点的存在性、唯一性及其全局指数稳定性。在没有假定激励函数有界、可微的情况下，得到了该类神经网络平衡点的存在性、唯一性及其在平衡点全局指数稳定的充分判据。该判据计算简便，且与时间滞后量无关，便于在实践中应用。文中给出了一个算例。

Global Exponential Stability of a Class of Neural Networks with Distributed Delays

Based on the theory of topological degree and properties of M-matrix, by constructing proper vector Lia- punov functions, the existence and uniqueness of the equilibrium point and its global exponential stability are investiga- ted for a class of neural networks with distributed and varying delays. Without assuming the boundedness and differen- tiability of the activation functions, several new sufficient criterions ascertaining the existence, uniqueness and global exponential stability of the equilibrium point of such neural networks are obtained. Since the criterion is independent of the delays and simplifies the calculation, it is easy to test the conditions of the criterion in practice. An example is given to demonstrate the feasibility of the criterion.