This paper suggests a design method of the model-following H${infty}$ control system having robust performance. This H${infty}$ control system is designed by applying genetic algorithm(GA) with reference model to the optimal determination of weighting functions and design parameter ${gamma}$ that are given by Glover-Doyle algorithm which can design H${infty}$ controller in the state space. These weighting functions and design parameter ${gamma}$ are optimized simultaneously in the search domain guaranteeing the robust performance of closed-loop system. The effectiveness of this H${infty}$ control system is verified by applying to the boiler-turbine control system.