Robust control of a lightly-damped system, such as the mechanical structure of a spacecraft, is a dilemma for control engineers. The shaker's table used for satellite vibration tests for qualification uses a sine sweep acceleration signal to characterize the satellite's frequency signature. The current control system presents strong oscillation while sweeping through high-frequency modes. Moreover, the process of fixing control parameters takes a long time leading to an increase in the testing costs. In this paper, a robust controller is proposed, based on an ∞ synthesis. This approach reduces the duration of vibration testing, and eliminates the vibration for any sine sweep rate, for all lower and higher modes. Moreover, the proposed controller is able to achieve good stability margins, a certain level of delay margin, and a small tracking error, which complies entirely with the specifications.