This paper introduces a computational methodology that adopted a method of Linear Quadratic Gaussian (LQG) controller as Automatic Voltage Regulator (AVR) and Governor to control the generator terminal voltage and the turbine speed. In this method the models were assumed to be Linear, depending on this method the controller power consumption was minimized depending on some performance index, which is assumed to be Quadratic. This method was taken into account the noise and the disturbance in

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... w, considered its distribution as Gaussian. The two degree of freedom (2DOF) structure was adopted, in which two controllers are used. The effectiveness of the proposed control action is demonstrated through some computer simulations on a Single-Machine Infinite-Bus (SMIB) power system. To accommodate stability requirements, a mathematical model for the generator and the turbine was derived based on the twoaxis theorem and starting from the swing equation. Results obtained show that adopting such a controller enhanced the steady state and transient stability.