A control design strategy to stabilize the improved three degrees-of-freedom nonlinear aeroelastic test apparatus (DOF NATA) model is proposed. The proposed numerical control design methodology for tensor product-type polytopic models can be executed systematically in a routine-like manner and preserves this property even if the model is extended with additional nonlinearities. The proposed methodology is capable of control performance optimization through the use of linear matrix inequalities and convex hull manipulation. It is shown by simulation of a perturbed model that the designed controller and observer are resilient to a variety of perturbations. The next step of the research is to design a stabilizing control solution to the same wing model with parameter uncertainties and the time delay included in the design phase and in the model, and thus guarantees on the robustness can be made.