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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Γ,使得由网络所确定的判别矩阵S(Γ,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.
In this paper, we study the global exponential stability of Sigmoid static continuous feedback neural networks under critical conditions.We use matrix measure theory to prove that for this type of neural network, if it satisfies the critical condition, that is, there exists positive definite matrix Γ, The definite discriminant matrix S (Γ, L) is semi-positive definite, then the network has a unique equilibrium state y ~ *, and when y ~ * is not a given point, y ~ * stabilizes the global exponential stability over R ~ N. Conclusions The noncritical exponential stability of the known sigmoid continuous feedback neural network is generalized without any additional conditions. It is also a great unity and extension of the results of the previous critical stability.