Mean square exponential stability of impulsive control stochastic systems with time-varying delay

In this Letter, we are concerned with the mean square exponential stability problem of an impulsive control stochastic system with time-varying delay. By employing the formula for the variation of parameters and estimating the Cauchy matrix, several criteria on mean square exponential stability are derived and the exponential convergence rate is estimated. The obtained criteria can be applied to stabilize the unstable continuous stochastic system by utilizing impulsive control. Two examples are also discussed to illustrate the efficiency of the obtained results.