This article presents a computationally efficient way of synthesizing linear parameter-varying (LPV) controllers. It reviews the possibility of a separate observer and state feedback synthesis with guaranteed performance and shows that a standard mixed sensitivity problem can be solved in this way. The resultant output feedback controller consists of an LPV observer, augmented with dynamic filters to incorporate integral control and roll-off properties, and an LPV state feedback gain. It is thus highly structured, which is beneficial for implementation. Moreover, it does not depend on scheduling parameter rates regardless of whether parameter-dependent Lyapunov matrices are used during synthesis. A representative control design for active flutter suppression on an aeroelastic unmanned aircraft demonstrates the benefits of the proposed method in comparison with state-of-the-art LPV output feedback synthesis.