Sigmoid型静态连续反馈神经网络的临界全局指数稳定性  

The Critically Exponential Stability for Static Continuous Recurrent Neural Networks with Sigmoidal Functions

作　　者：乔琛[1] 徐宗本[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049

出　　处：《应用数学学报》2012年第6期961-971,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(11101327);中央高校基本科研业务费专项资金(xjj20100087;2011jdhz30)资助项目

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 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.

关 键 词：反馈神经网络 Sigmoid型 临界分析 全局指数稳定性 

分 类 号：O231[理学—运筹学与控制论]