Global stabilization via time-varying output-feedback for stochastic nonlinear systems with unknown growth rate

This paper considers the global stabilization via time-varying output-feedback for a class of stochastic nonlinear systems. Different from the related existing literature, the systems possess serious uncertainties/unknowns which are reflected in the uncertain control coefficient and the unknown growth rate of the unmeasured states dependent growth. To deal with these serious uncertainties/unknowns, a time-varying framework, rather than an adaptive one, is proposed in this paper since the latter has not been successfully employed in the topic. Detailedly, due to the absence of precise information on the control coefficient, time-varying K-filters are introduced to construct the unmeasured system states. By a delicate time-scaling transformation, a time-scaled entire system is derived, and from which, the design scheme of a time-varying output-feedback controller is developed by backstepping method and time-varying technique. It is shown that all signals of the resulting closed-loop system converge to zero a.s., and furthermore, when serious time-variations exist as well, it suffices to find a fast enough time-varying gain for the control design scheme. A simulation example is given to show the effectiveness of the theoretical results.