时滞Cohen-Grossberg神经网络的全局稳定性

Global Stability Analysis of Cohen-Grossberg Neural Networks with Unbounded Time Delays

为将神经网络应用于最优化问题的求解,对具有无穷时滞的Cohen-Grossberg神经网络平衡点的存在性、唯一性和全局渐近稳定性进行了探讨.在不假设激活函数有界性、单调性和可微性的情况下,得到了系统平衡点的存在性条件.利用向量Liapunov函数法,构造适当的含有无穷时滞的微分-积分不等式,并分析了微分-积分不等式的稳定性,得到了Cohen-Grossberg神经网络系统全局渐近稳定性的判据.通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M-矩阵,即可得到Cohen-Grossberg神经网络系统的全局渐近稳定性.最后给出了一个算例,以说明该判据的正确性.

In order to apply the neural networks to optimization problems, the conditions ensuring the existence, uniqueness and global asymptotical stability of the equilibrium point of Cohen-Grossberg neural networks （CGNN）with unbounded time delays were investigated. Without assuming the boundedness, monotone and differentiability of the activation functions, the existence conditionof the equilibrium point of CGNN was obtained. Using the vector Liapunov function method, the intero- differential inequalities with unbounded time delays were constructed, and the stability of the intero- differential inequalities were analyzed to obtain the criteria for the global asymptotical stability of the equilibrium point. Based on the criteria, the global asymptotic stability of CGNN can be get by judging whether the matrix constructed by the weighed coefficients, self-feedback functions and activation functions of CGNN is an M-matrix. Finally, an example was given to testify the validity of the criteria.