Absolute stability analysis in cellular neural networks with variable delays and unbounded delay

In this paper, the existence and uniqueness of the equilibrium point and absolute stability of a class of cellular neural networks with globally Lipschitz continue activation functions are investigated. The neural networks contain both variable and unbounded delays. The necessary and sufficient condition for the existence and uniqueness of the equilibrium point of the neural networks is obtained. By constructing proper vector Liapunov functions, nonlinear integrodifferential inequalities involving both variable delays and unbounded delay, which are corresponding to the neural networks, are established. By using M-matrix theory and qualitative property of the integrodifferential inequalities, the sufficient conditions for absolute stability (global asymptotic stability) are obtained.