Aeroelastic control functions, such as active gust load alleviation, enable lighter structural designs for future commercial aircraft and thereby support reductions in fuel consumption and emissions. Traditionally, these functions are developed separately, as add-ons to the primary flight control system, relying on a clear frequency separation between rigid-body and flexible aircraft dynamics. As aircraft structures become more flexible, this separation no longer holds, resulting in coupled dynamics and motivating an integrated design. This paper presents an integrated control law design using -synthesis robust control, a powerful method that allows for efficient trade-offs between multiple performance and robustness objectives. The design jointly addresses gust load alleviation as an aeroelastic control function and command augmentation as a primary flight control function. Controller performance is validated through wind tunnel experiments on a flexible, clamped wing. Although this setup prevents direct testing of primary flight control functions, representative tasks are defined to enable meaningful experimental validation. Wind tunnel results demonstrate the effectiveness of the integrated control law.