In this paper the implementation of a robust Model Predictive Control (MPC) algorithm for constrained uncertain discrete-time linear systems subject to norm-bounded model uncertainties is used to deal with the control allocation problem of an High Altitude Performance Demonstrator (HAPD) unmanned aircraft with redundancy control surfaces. Specifically, the HAPD nonlinear model is described by means of LFR differential inclusions achieved via embedding arguments while the surface deflection amplitude limitations are formulated in terms of convex constraints. As a consequence, the overall control problem can be recast in terms of Linear Matrix Inequalities (LMIs) that are affordable from a computational point of view.