Abstract: The behavior of building structures is naturally uncertain because of the numerous uncertainties of seismic disturbances and structural parameters. In this paper, we present a new robust and non-fragile H_∞ control approach that 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 the use of an efficient solution procedure based on linear matrix inequalities (LMI). Such a new robust and non-fragile H_∞ controller for buildings can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties. In view of the uncertainty of seismic disturbance and the model errors of the building structure, a three-storey shear building model containing active brace systems is analyzed. 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 and non-fragile H_∞ controllers is remarkable and robust. Considering reasonable parameter values, the controller can acquire considerably better performance of robust and non-fragile than traditional H_∞ controller under the optimal response quantities. Therefore, the robust and non-fragile H_∞ control method is quite promising for practical implementations of active control systems on seismically excited linear structures.