Time-Varying Stabilizers for Stochastic Systems with no Unforced Dynamics

This paper is concerned with the stabilizability of nonlinear stochastic systems with no unforced dynamics. Sufficient conditions allowing to design explicitly time-varying feedback laws which render such systems asymptotically stable in probability are given. The techniques used in this work involve the stochastic Lyapunov analysis combined with the stochastic version of the La Salle invariance principle. The interest of our results is that the systems considered in the present paper cannot in general be stabilized via time-invariant feedback laws.