On global asymptotic stability of neural networks with discrete and distributed delays

Abstract

In this Letter, the global asymptotic stability analysis problem is investigated for a class of neural networks with discrete and distributed time-delays. The purpose of the problem is to determine the asymptotic stability by employing some easy-to-test conditions. It is shown, via the Lyapunov–Krasovskii stability theory, that the class of neural networks under consideration is globally asymptotically stable if a quadratic matrix inequality involving several parameters is feasible. Furthermore, a linear matrix inequality (LMI) approach is exploited to transform the addressed stability analysis problem into a convex optimization problem, and sufficient conditions for the neural networks to be globally asymptotically stable are then derived in terms of a linear matrix inequality, which can be readily solved by using the Matlab LMI toolbox. Two numerical examples are provided to show the usefulness of the proposed global stability condition.