Global control for a class of planar stochastic nonlinear systems with unknown output gain

This paper addresses the problem of global asymptotical stabilization via output feedback for a class of planar stochastic nonlinear systems whose output gain is not precisely known. We first design an observer and use the estimated states to construct a controller to globally stabilize the nominal linear system without considering perturbing nonlinearities. Then we apply the homogeneous domination approach to design a homogeneous observer and controller with an appropriate choice of scaling gain to render the planar stochastic nonlinear system globally asymptotically stable in probability.