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Stability analysis of nonlinear stochastic differential delay systems under impulsive control. (English) Zbl 1248.90030
Summary: In this Letter, we study the stability of nonlinear stochastic differential delay systems under impulsive control. First, we construct an impulsive control for a nonlinear stochastic differential delay system. Then, the equivalent relation between the stability of the nonlinear stochastic differential delay system under impulsive control and that of a corresponding nonlinear stochastic differential delay system without impulses is established. Third, some sufficient conditions ensuring various stabilities of the nonlinear stochastic differential delay systems under impulsive control are obtained. Finally, an example is also discussed to illustrate the effectiveness of the obtained results.

MSC:
90B15 Stochastic network models in operations research
49N25 Impulsive optimal control problems
37H10 Generation, random and stochastic difference and differential equations
35B35 Stability in context of PDEs
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