This paper presents the design of a novel control strategy of a Power System Stabilizer (PSS) for generators in multimachine electric power systems using the Linear Quadratic Gawssian (LQG) control technique. The controller combines both the excitation and governor control loops. The technique is applied using a sample power system which includes a number of generators connected to a large power system. An optimal full state controller has been designed and a state observer is included using Kalman Filter theory. A comprehensive stability analysis and time domain performance analysis of the system with the new controller have been presented.  The results prove the robustness and powerful of proposed LQG controller in improve stability margins and adding positive with a noticeable reduction in settling time.