Feedback Stabilization of Affine in the Control Stochastic Differential Systems by the Control Lyapunov Function Method

Abstract

The purpose of this paper is to study the asymptotic stability in probability of affine in the control stochastic differential systems. Sufficient conditions for the existence of control Lyapunov functions leading to the existence of stabilizing feedback laws which are smooth, except possibly at the equilibrium point of the system, are provided.