Abstract: This paper is concerned with the robust mean square stability for stochastic differential systems with multiple time-varying delays and nonlinear perturbation in memory state feedback controller. By establishing a Lyapunov-Krasovskii functional, using the It$\hat{\rm o}$ formula, introducing appropriate free-weighting matrices, making use of an integral inequality and an analytical technique, based on the linear matrix inequality (LMI) and Schur complement theorem, the robust mean square asymptotically stability and the robust mean square  exponentially stability for the system are obtained. In addition, the corresponding state feedback controllers are constructed. The results are dependent on delays and stochastic perturbation, and extend the existing results.

Key words: nonlinear perturbation, stochastic differential system with delays, feedback control, linear matrix inequality (LMI), robust mean square stability