Ｈ∞ norm γ reflects the disturbance attenuation level of robust control systems. This paper investigates its influences on the performances of the closedloop control systems, such as Ｈ２norm and dynamic characteristics including responses by initial states and disturbance excitations. Since Ｈ∞norm represents only one dynamic performance index of control systems,the others may not be optimized when Ｈ∞norm does. According to numerical results in the paper, the optimal Ｈ∞norm is almost a singular value for the other dynamic characteristics, which would vary sharply when parameter γ varies near to its minimum value γopt. All the numerical results demonstrate that satisfactory performances of control systems depend on the optimization of multiple parameters simultaneously. And the selection of design parameter γ deserves further studies.