A Passive System Approach to Feedback Stabilization of Nonlinear Control Stochastic Systems

Abstract

The purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws. In particular, we prove that, as in the case of stochastic differential systems affine in the control, one can compute stabilizing feedback laws provided the unforced stochastic differential system is Lyapunov stable in probability and some rank conditions are fulfilled. Some well-known stabilization results for stochastic differential systems affine in the control proved in the literature are extended to nonaffine nonlinear control stochastic differential systems.