In this paper, fixed-order robust H-infinity controller design for systems with ellipsoidal parametric uncertainty based on parameter dependent Lyapunov functions is studied. Using the concept of Strictly Positive Realness (SPRness) of transfer functions, a fixed-order robust control design method in terms of solution to a set of Linear Matrix Inequalities (LMIs) is proposed. Since, controller parameters are decision variables, any controller structure, such as PID, can be considered. The weighted infinity-norm of closed loop sensitivity functions are considered as performance specification in the synthesis problem. The simulation results show the effectiveness of the proposed method.