Global asymptotic stability of delayed neural networks with discontinuous neuron activations

This paper investigates a class of delayed neural networks whose neuron activations are modeled by discontinuous functions. By utilizing the Leray–Schauder fixed point theorem of multivalued version, the properties of M-matrix and generalized Lyapunov approach, we present some sufficient conditions to ensure the existence and global asymptotic stability of the state equilibrium point. Furthermore, the global convergence of the output solutions are also discussed. The assumptive conditions imposed on activation functions are allowed to be unbounded and nonmonotonic, which are less restrictive than previews works on the discontinuous or continuous neural networks. Hence, we improve and extend some existing results of other researchers. Finally, one numerical example is given to illustrate the effectiveness of the criteria proposed in this paper.