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A comprehensive analysis of aeroelastic systems has shown that these systems exhibit a broad class of pathological response regimes when certain types of nonlinearities are included. We propose a design method of a state-dependent nonlinear controller for aeroelastic systems that includes polynomial structural nonlinearities. The method is based on recent numerical methods such as tensor product model transformation and parallel distributed compensation. As an example, a controller is derived that ensures the global asymptotic stability of a prototypical aeroelastic wing section via one control surface. Alternative solution with one control surface and global asymptotic stability does not exist so far. Numerical simulations are used to provide empirical validation of the control results. The effectiveness of the controller design is compared with former approaches.