In our previous paper, we developed a robust saturation controller for the linear time-invariant (LTI) system involving both actuators saturation and structured real parameter uncertainties. This controller can only guarantee the closed-loop robust stability of the system in the presence of actuators saturation. But we cannot analytically make any comment on control performance of this controller. In this paper, we suggest a method to use linear matrix inequality (LMI) optimization problem which can analytically explain control performance of this robust saturation controller only in nominal system. The availability of design method using LMI optimization problem for this robust saturation controller is verified through a numerical example for the building with an active mass damper (AMD) system.