On global asymptotic stability of recurrent neural networks with time-varying delays

摘要

In this paper, by constructing a new Lyapunov functional, and using M-matrix and topological degree tool, problem of the global asymptotic stability (GAS) is discussed for a class of recurrent neural networks with time-varying delays. Some simple and new sufficient conditions are obtained ensuring existence, uniqueness of the equilibrium point and its GAS of the neural networks. Some previous works are improved. In addition, this condition does not require the activation functions to be differentiable, bounded and monotone nondecreasing and the weight-connected matrices to be symmetric. The neural network model considered in this paper include the delayed Hopfield neural networks, bidirectional associative memory networks and delayed cellular neural networks as its special cases.