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Zbl 1229.92006
Ma, Li; Da, Feipeng
Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays. (English)
[J] Phys. Lett., A 373, No. 25, 2154-2161 (2009). ISSN 0375-9601

Summary: In this Letter, the mean-square exponential stability problem for stochastic Hopfield neural networks with both discrete and distributed time-varying delays is investigated. By choosing a modified Lyapunov-Krasovskii functional, a delay-dependent criterion is established such that the stochastic neural network is mean-square exponentially stable. The derivative of discrete time-varying delay $h(t)$ satisfies $\dot{h}\leq \eta$ and the decay rate $\beta $ can be any finite positive value without any other constraints. The assumptions given in this Letter are more general than the conventional assumptions (i.e., $\dot{h}((t)\leq \eta < 1$ and $\beta $ satisfies a transcendental equation or an inequality). Finally, numerical examples are provided to illustrate the effectiveness of the proposed sufficient conditions.

MSC 2000:: *92B20 General theory of neural networks
68T05 Learning and adaptive systems
60K99 Special processes
37N25 Dynamical systems in biology
34K60 Applications of functional-differential equations

Keywords: stochastic systems; time-varying delay systems; neural networks; exponential stability; linear matrix inequality

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