We characterize an input-affine model of the UAV DarkO: a convertible drone designed and developed at the Ecole Nationale de L'Aviation Civile (ENAC) in Toulouse (France). Starting from a nonlinear model available in the literature, we present an approximate input-affine nonlinear model, whose dynamics simplifies the control design task. For this simplified model, we characterize the hovering equilibria in the absence of wind, and we derive the corresponding linearized dynamics. Then present a hysteresis-based switching mechanism combining a nonlinear feedback (providing a large basin of attraction) with a linearized feedback (providing improved performance but a smaller basin of attraction). Simulation results, using the original nonlinear model, confirm the effectiveness of the proposed feedback design.