中文摘要：

本文致力于研究Sigmoid型静态连续反馈神经网络在临界条件下的全局指数稳定性．我们利用矩阵测度理论证明：对于该类型神经网络，若其满足临界条件，即存在正定矩阵r，使得由网络所确定的判别矩阵S（r，L）半正定，则网络具有唯一平衡态y^＊，且当y^＊不为某一给定点时，y^＊在R^N上全局指数稳定．所获结论在不增加附加条件的情况下一致地推广了已知Sigmoid型连续反馈神经网络的非临界指数稳定性结论，同时是已有临界稳定性结果的极大统一和延伸．

英文摘要：

In the paper, we denote to investigate the critically exponential stability of static continuous recurrent neural networks with Sigmoidal functions. By using matrix measure theory, we proved that if there exists a positive definite diagonal matrix F, such that S（F, L）, the matrix defined by the network, is nonnegative definite, then the network has a unique equilibrium state y^＊, and when y^＊ is not one given point, then y^＊ is globally exponential stability on RN. The obtained results not only improved the existing non- critical conclusions on global stability of the neural networks with sigmoidal functions, but also unified and extended the known critical stability results to a largest extent.