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This paper introduces an application of genetic algorithm (GA) to determine weighting matrices Q and R elements in linear quadratic regulator (LQR) optimization process. The weighting matrices, Q and R are the most important components in LQR optimization and determine the output performances of the system. Commonly, a trial-and-error method has been used to construct the elements of these matrices. This method is simple, but very difficult to choose the best values that have good control performances. Because of this, the Bryson method can be employed to give better results. In this paper, we use GA to construct the weighting matrices Q and R properly with help of Bryson method. This idea gives a new alternative procedure in time varying feedback control to improve the stability performance. This design implemented in an inverted pendulum as a benchmark control problem.