In this paper we consider a stochastic nonlinear system under regime switching. Given a system ( ) ( ( ), ( ), ) x t f x t r t t in which f satisfies so-called one-side polynomial growth condition. We introduce two Brownian noise feedbacks and stochastically perturb this system into
t x t x t W t t x t W t. It can be proved that appropriate noise intensity may suppress the potentially explode in a finite time and ensure that this system is almost surely exponentially stable although the corresponding system without Brownian noise perturbation may be unstable system. d