Global Output-Feedback Stabilization for a Class of Stochastic Non-Minimum-Phase Nonlinear Systems

In this paper, the output-feedback stabilization problem is investigated for the first time for a class of stochastic nonlinear systems whose zero dynamics may be unstable. Under the assumption that the inverse dynamics of the system is stochastic input-to-state stabilizable, a stabilizing output-feedback controller is constructively designed by the integrator backstepping method together with a new reduced-order observer design and the technique of changing supply functions. It is shown that, under small-gain type conditions, the resulting closed-loop system is globally asymptotically stable in the probabilistic sense. The obtained results extend the existing methodology from deterministic systems to stochastic systems.