| The earthquake, the natural phenomenon which had done great harmto the human beings, has always threatened the security of life andfortune of humanity since human beings appeared on Earth. A mass ofresearches and studies have been made in order to avoid the damage ofbuildings aroused by the earthquake. As the development of humanity'ssciences and technologies, the conception of structural vibration controlbrings a new hope to the scholars and specialists. They have beeninvolved in the new domain theoretically and experimentally and begunto apply it practically. However, it is very difficult to obtain the accurate mathematicalmodel due to the immense body of buildings and the special load carriedby the seism. First, it is necessary to simplify the actual structure.Second, non-linear factors should be linearized. Third, the physicalparameters of structure vary during the earthquake. Fourth, the load ofseism is random. Thus, the robustness of the control system is verycrucial and the robust control theory is concerned and developed widelyand constantly. The sliding mode control can constrain the system to reach or closeup to the status trajectory of the sliding mode and skip from one status toanother instantly according the status of the system. Because the slidingmode is designable and it is not concerned with the perturbation of theparameters of the structure and the varieties of the disturbance, thesliding mode is absolutely self-adaptive. The simulations demonstratethis control method can weaken the vibration effectively and is robustvery much. The H_∞ -norm of the transfer function between one signal andanother of the system is considered as the optimized target and the worstinstance is minimized by the H_∞ control theory. The simulations showthat the vibration of the structure is diminished effectively and thecontrol method is not sensitive to the perturbation of the parameters ofthe structure and the varieties of the disturbance and it is robust.
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