This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous （nonsmooth） output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.
In this paper, the global asymptotic stabilization by output feedback is investigated for a class of uncertain nonlinear systems with unmeasured states dependent growth. Compared with the closely related works, the remarkableness of the paper is that either the growth rate is an unknown constant or the dimension of the closed-loop system is significantly reduced, mainly due to the introduction of a distinct dynamic high-gain observer based on a new updating law. Motivated by the related stabilization results, and by skillfully using the methods of universal control and backstepping, we obtain the design scheme to an adaptive output-feedback stabilizing controller to guarantee the global asymptotic stability of the resulting closed-loop system. Additionally, a numerical example is considered to demonstrate the effectiveness of the proposed method.
