Robustness of exponential stability of stochastic differential delay equations

Regard the stochastic differential delay equation dx(t)=[(A+A~(t))+(B+B~(t-/spl tau/))x(t-/spl tau/)] dt+g(t, x(t), x(t-/spl tau/))dw(t) as the result of the effects of uncertainty, stochastic perturbation, and time lag to a linear ordinary differential equation x/spl dot/(t)=(A+B)x(t). Assume the linear system is exponentially stable. In this paper we characterize how much the uncertainty, stochastic perturbation, and time lag the linear system can bear such that the stochastic delay system remains exponentially stable. The result can also be extended to nonlinear systems.