This paper investigates the global asymptotical stabilization using sampled-data output feedback (i.e., not all state information is available at the output) for a class of nonlinear systems which have uncontrollable and unobservable linearizations around the origin. A homogeneous version of Gronwall-Bellman inequality is introduced as the essential tool to estimate trajectory of nonlinear sampled-data control systems between two successive sampling instants. With the help of this new tool as well as the homogeneous domination approach, a sampled-data observer-based controller is constructed to globally asymptotically stabilize the origin of the nonlinear system under a homogeneous growth condition. (C) 2018 Elsevier Ltd. All rights reserved.