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Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. (English) Zbl 1181.93068
Summary: This Letter is concerned with the global asymptotic stability analysis problem for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-delays. By utilizing a Lyapunov-Krasovskii functional, using the well-known $S$-procedure and conducting stochastic analysis, we show that the addressed neural networks are robustly, globally, asymptotically stable if a convex optimization problem is feasible. Then, the stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. The main results are also extended to the multiple time-delay case. Two numerical examples are given to demonstrate the usefulness of the proposed global stability condition.
##### MSC:
 93D09 Robust stability of control systems 68T05 Learning and adaptive systems
##### Software:
LMI toolbox; LMI Control Toolbox