随机延时细胞神经网络的几乎必然指数稳定性

Almost Sure Exponential Stability of the Stochastic Delayed Cellular Neural Networks

依据细胞神经网络的输出函数特征,将状态空间分解成子区域,研究了一类随机延时细胞神经网络在噪声环境下的几乎必然指数稳定性.当细胞神经网络模型的扰动项满足Lipschitz条件时,得到一些几乎必然指数稳定的代数准则.如果细胞神经网络的平衡点是子区域的内点,并且与这个平衡点相关的矩阵有一个稳定度使扰动稳定,则细胞神经网络的平衡点仍保持指数稳定的性质.所有结果只需计算网络的平衡点与矩阵的特征值.

Almost sure exponential stability of a class of stochastic delayed cellular neural networks in the noise environment is researched by dividing the state space into sub-regions according to the characters of output functions of the network. Some algebraic criterion of almost sure exponential stability are obtained when the disturbance term of the network satisfies the Lipschitz condition. The equilibrium point of the network still remains the exponential stability if the equilibrium point is a interior point of the sub-region and the matrix related to the equilibrium point has a stable degree stabilize the perturba- tion. The equilibrium point of the network and the eigenvalue is only need to get the result.