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The stability of nonlinear stochastic delay systems with applications. (Chinese. English summary) Zbl 0972.34070

Summary: In the first part of this paper the authors consider a family of nonlinear stochastic delay systems with uncertainties. For such systems, they establish sufficient criteria for the exponential stability in mean square and the almost sure exponential stability. These criteria are independent of delay. In the second part, the authors apply these sufficient conditions to a class of stochastic delay neural networks with uncertainties and obtain practical criteria to test exponential stability of these stochastic delay neural networks. The results are generalizations of some recent ones reported in the literature. Finally, a numerical example is given to illustrate the effectiveness of the obtained criteria.

MSC:

34K50 Stochastic functional-differential equations
34K20 Stability theory of functional-differential equations
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