Stability of linear stochastic differential delay systems under impulsive control

In this study, the authors investigate stability of stochastic differential delay systems under impulsive control. First, an impulsive control for a kind of linear stochastic differential delay system is constructed. Then, the authors point out that different kinds of stability of linear stochastic differential delay systems under impulsive control is equivalent respectively, to the stability of the corresponding linear stochastic differential delay systems without impulses. Finally, several stability criteria of a class of linear stochastic differential delay systems under impulsive control are presented. Moreover, an example is also discussed to illustrate the effectiveness of the proposed results.