On global asymptotic stability of neural networks with discrete and distributed delays. (English) Zbl 1345.92017

Summary: 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.


92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology


Matlab; LMI toolbox
Full Text: DOI Link


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