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This paper describes a LQG robust controller for the load frequency control of an electrical power system. The controller is used in order to achieve robust stability and good dynamic performance against the variation of power system parameters and its load. The application of the proposed LQG robust control scheme is implemented through the simulation of a single area power system model. The proposed robust controller for power systems stability is designed using Matlab/Simulink program. Simulation results confirm the performance of the proposed controller for the electrical power system.