This paper presents a particular class of a convertible micro aerial vehicle (MAV) with fixed wings, the so-called Quad Tiltrotor aircraft. This aircraft is able to change its flight configuration from hover to level flight and vice versa by means of a transition maneuver. In this first part of the research, the hover dynamics of the Quad Tiltrotor is investigated. Dynamical model and nonlinear control based on Lyapunov design are studied. The presented approach focuses on the problem of finding a control law capable of stabilizing the aircraft's position. Some simulations results are given, which demonstrate the effectiveness of the controller. Further, some experimental results are presented tested on the Quad Tiltrotor experimental platform.