This paper proposes a robust H2 feedback controller design for damping power system oscillations over a wide range of operating conditions. Robust H2 control technique based power system controller is developed for both excitation system and speed governor control. The effectiveness of the proposed power system controller is validated by a simple power system composed of a synchronous generator connected to an infinite bus through a transmission line. A comparison between power system responses at variety of operating conditions using the proposed H2 controller and Linear Quadratic Regulator LQR control is obtained. The digital simulation results prove the powerful of the proposed power system controller based on H2theory in terms of fast power system mechanical oscillation damping over a wide range of operating conditions with system uncertainty and parameters change.