Global asymptotic stability of delayed neural networks with discontinuous neuron activations

In this paper, we integrate a class of delayed neural networks with discontinuous activations, which are not supposed to be bounded or nondecreasing. Conditions of existence of an equilibrium point are established by means of the Leray–Schauder theorem of set-valued maps. Then, the existence of solutions is proved based on viability theorem. Furthermore, global asymptotical stability of the networks is studied by using Lyapunov–Krasovskii stability theory. The results of global asymptotical stability are in term of linear matrix inequality. The obtained results extend previous works on global stability of delayed neural networks with discontinues activations.