In view of the numerous uncertainties of seismic disturbances and structural parameters, the irregular building structure is uncertain. In this paper, a new robust optimal H∞ controller for irregular buildings is designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties. Such a control method can provide a convenient design procedure for active controllers to facilitate practical implementations of control systems through the use of a quadratic performance index and an efficient solution procedure based on linear matrix inequality (LMI). To verify the effectiveness of the control method, a MDOF (multipledegree-of-freedom) eccentric building structure with two active mass damper (AMD) systems on the orthogonal direction of the top storey subjected to bi-directional ground motions is analyzed. In the simulation, the active control forces of the AMD systems are designed by the robust optimal H∞ control algorithm, and the structural system uncertainties are assumed in the system and input matrices. The simulation results obtained from the proposed control method are compared with those obtained from traditional H∞ control method, which shows preliminarily that the performance of robust optimal H∞ controllers is remarkable and robust. Therefore, the robust optimal H∞ control method is quite promising for practical implementations of active control systems on seismically excited irregular buildings.
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