A linear parameter dependent approach for designing a constant output feedback controller, for a linear time-invariant system with uncertain parameters that achieves a minimum bound on. either the H-2 or the H-infinity performance level is introduced. Assuming that the uncertain parameters reside in a given polytope a parameter dependent Lyapunov function is described which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope.