摘要
分析了Cohen-Grossberg神经网络的指数稳定性(局部指数稳定和全局指数稳定).给出了基于矩阵测度的判定Cohen-Grossberg神经网络的指数稳定的充分条件.并且对于局部指数稳定的平衡点,给出了其吸引域的估计;对于全局指数稳定的平衡点,给出了其指数收敛的速率.该结果可以用于神经网络容错能力的估计以及其指数收敛速率的估计,因此在设计Cohen-Grossberg神经网络中具有很重要的现实意义.
Exponential stability （local exponential stability and global exponential stability） was analyzed for Cohen-Grossberg neural networks. Simple sufficient conditions in the form of matrix measure were derived for ascertaining the local exponential stability or the global exponential stability for Cohen-Grossberg neural networks. Moreover, for the locally exponentially stable equilibrium point, its attraction region was estimated; for the globally exponentially stable equilibrium point, its convergence rate was assessed. The proposed results can be used for the evaluation of fault-tolerance capability and the estimation of exponential decay rate of the networks, and are hence of practical significance for designing Cohen-Grossberg neural networks.
基金
Supported by the grants from the National Natural Science Foundation of China(61004043)
the Specialized Research Fund for the Doctoral Program of Higher Education(2009092120066)
