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

Wang, Zidong; Liu, Yurong; Liu, Xiaohui

Phys. Lett., A 345, No. 4-6, 299-308 (2005).

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.

MSC:

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

Keywords:

neural networks; distributed delays; discrete delays; Lyapunov-Krasovskii functional; global asymptotic stability; linear matrix inequality

Software:

Matlab; LMI toolbox

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