The paper shows an example when the tightening of the convex hull determined by the vertexes of the polytopic Tensor Product model representation of a given quasi Linear Parameter Varying state-space model leads to feasible Linear Matrix Inequality based control design. In addition the paper unveils that the relaxation of the Tensor Product model complexity interferes also with the Linear Matrix Inequality feasibility results. The example at hand consists of the complex Nonlinear Aeroelastic Test Apparatus model of the three degree of freedom aeroelastic wing section model including Stribeck friction. The relaxation and convex hull tightening is based on the concept of the Tensor Product model transformation.