A stochastic version of Vidyasagar theorem on the stabilization of interconnected systems

The purpose of this paper is to provide sufficient conditions for the feedback asymptotic stabilization in probability for a class of affine in the control nonlinear stochastic differential systems.In fact, under the assumptions stated in this paper we prove the existence of a control Lyapunov function that according to the stochastic version of Artstein's theorem guarantees the asymptotic stability in probability by means of a state feedback law that is smooth except eventually at the equilibrium.This result generalizes the well-known theorem of Vidyasagar concerning the feedback stabilization problem for interconnected control systems.