This paper concerned with the problem of optimization of parameters for the flexible structure. The structure has 4 stories and each story is modeled such that it has a single degree of freedom in the transverse direction and one more degree of freedom in the angle of torsion around the centroid of the story. The model of structure, absorber and stroke are combined such that the number of state is 30. The process of optimization is to minimize the H ∞ -norm from closed loop transfer function of the system which implies suppressing the magnitude peaks vibration of the frequency response. Parameters optimization of flexible structure system becomes an H ∞ -output feedback problem. This problem is transformed to Bilinear Matrix Inequality problem and then it is solved by using the genetic algorithm.