Flutter is an aeroelastic phenomenon affecting flexible structures in a fluid flow and may lead to unstable oscillations and to critical structural damage. This paper concerns the design of a controller to provide active flutter suppression on an unmanned flexible-wing demonstrator, currently under construction. The aircraft models used in the control design are obtained using a combination of balanced and modal reduction techniques from a high-fidelity nonlinear aeroservoelastic model, and include information about actuator and sensor dynamics as well as the phase loss introduced by the flight control computer. The controller is synthesized by posing and solving a weighted H∞-norm optimization problem with the goal to provide damping for the flutter modes and extend the flight envelope above the open-loop flutter speed. The paper concludes with a thorough analysis and verification of the performance achieved by the closed-loop system, including simulations with the high-fidelity nonlinear model of the actual maneuvers that will be performed by the unmanned demonstrator during future flight tests.