This paper proposes a linear parameter varying (LPV) model reference-based control for fixed-wing unmanned aerial vehicles (UAVs), which achieves agile and high performance tracking objectives in extended flight envelopes, e.g. when near stall or deep stall flight conditions are considered. Each of the considered control loops (yaw, pitch and airspeed) delivers an error model that can be reshaped into a quasi-LPV form through an appropriate choice of the scheduling variables. The quasi-LPV error models are suitable for designing error feedback controllers using linear matrix inequalities (LMIs), which are derived within the quadratic Lyapunov framework. Simulation results are used to show the effectiveness of the proposed approach.