This paper addresses the design of full order linear dynamic output feedback controllers for flexible structures. Unstructured H-infinity uncertainty models are introduced for systems in modal coordinates and in reduced order form. Then a controller is designed in order to minimize a given H-2 performance function while keeping the maximum supported H-infinity perturbation below some appropriate level. To solve this problem we develop an algorithm able to provide local optimal solutions to optimization problems with convex constraints and non-convex but differentiable objective functions. A controller design procedure based on a trade-off curve is proposed and a simple example is solved, providing a comparison between the proposed method and the usual minimization of an upper bound to the H-2 norm. The method is applied to two different flexible structure theoretical models and the properties of the resulting controllers are shown in several simulations.66557598