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Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays. (English) Zbl 1257.34063

Summary: This paper is concerned with stability analysis of uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and to belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the time-varying delays which may be differentiable and may not be differentiable are considered in this paper. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay/interval-dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), by introducing some free-weighting matrices. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed LMI conditions.

MSC:

34K50 Stochastic functional-differential equations
34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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