具有无穷时滞高阶模糊Cohen-Grossberg神经网络的稳定性

利用M矩阵理论和矩阵不等式、矢量Lyapunov 函数法,研究了一类具有无穷时滞的高阶模糊Cohen-Grossberg神经网络的全局指数稳定性.在不要求神经网络激活函数的单调递增性、可微性及Lipschitz连续等假设条件下,得到了该类神经网络平衡点的存在性和唯一性,以及全局指数稳定性的代数判据.该判据为M矩阵的显式形式,与系统的时间滞后以及反应扩散无关,易于在应用中进行检验.最后,通过仿真算例,验证了该方法的正确性和有效性. 

Stability of High Order Fuzzy Cohen-Grossberg Neural Networks with Unbounded Time Delays

Using M-matrix theory, matrix inequality and vector Lyapunov methods, the global exponential stability of a class of high-order fuzzy Cohen-Grossberg neural networks with unbounded time delays was investigated. Without assuming the monotonicity, differentiability and Lipschitz continuity of the active functions, the algebraic criteria ensuring existence, uniqueness and exponential stability of the equilibrium point in the neural networks were obtained. The criteria is independent to the reaction diffusion and the time delays of neural networks by the explicit form of M-matrix,and easy to be checked in application. Finally, the correctness and validity of the methods was verified by a numerical example.