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Robust stability for stochastic Hopfield neural networks with time delays. (English) Zbl 1122.34065
The Hopfield neural network is described by a stochastic delay differential equation of the form $$dx(t)=(-Ax(t)+W l(x(t-h)))dt+(Cx(t)+Dx(t-h))dw(t).$$ Here $A,W,C,D$ are matrices with certain properties, $l$ is a Lipschitz continuous neuron activity function and $w$ is a Brownian motion. It is shown that certain explicit matrix inequalities imply that the equilibrium solution is robustly, globally, asymptotically stable in the mean-square sense.

##### MSC:
 34K50 Stochastic functional-differential equations 34K20 Stability theory of functional-differential equations 93D09 Robust stability of control systems 92B20 General theory of neural networks (mathematical biology)
LMI toolbox
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##### References:
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