Global stabilization via time-varying adaptive output-feedback for a class of uncertain stochastic nonlinear systems

This paper considers the global stabilization via output-feedback for a class of uncertain stochastic nonlinear systems. Different from the closely related literature, the systems possess unmeasured states time-varying dependent growth with growth rate of polynomial-of-output multiplying an unknown constant. To deal with the serious unknowns, the serious time-variations and the heavy nonlinearities simultaneously, adaptive technique and time-varying technique are used in combination. Detailedly, time-varying technique is adopted to compensate the serious unknowns and the serious time-variations, and a delicate dynamic gain is constructed via adaptive technique to handle the polynomial-of-output in the growth rate. Then, a time-varying dynamic-gain observer is constructed, and based on this, a time-varying dynamic-gain output-feedback controller is designed, such that all signals of the closed-loop system are bounded a.s., and all states of the closed-loop system converge to zero a.s..