This paper proposes a control design strategy, encompassing trajectory tracking and path following, for a category of convertible aircraft with fixed wings and vectorized thrust, as exemplified by the Harrier jet aircraft and the V-22 Osprey. The approach relies on, and extends, previous works on the control of hovering vehicles (helicopters, quadrotors,...), axisymmetric devices (rockets, missiles,...), and fixed-wing aircraft (airplanes). In particular it exploits a common nonlinear model of aerodynamic forces exerted on the vehicle, both simple and representative of the underlying physics. Besides the unifying property of this approach, the proposed solution addresses the delicate transition problem between hovering and cruising flight, and thus the concomitant thrust tilting issue, in a novel manner with the possibility of continuously minimizing the thrust intensity, and thus energy expenditure.