Finite frequency H∞H∞ control for building under earthquake excitation

This paper deals with the problem of H∞H∞ control for seismic-excited buildings in finite frequency domain. The objective of designing controllers is to guarantee the asymptotic stability of the closed-loop system and attenuate the disturbance from earthquake excitation. After analyzing the frequency spectrum of some typical earthquakes, a frequency range in which earthquakes have a higher strength and lead to more serious damage to buildings, 0.3–8.8 Hz, is confirmed. Based on H∞H∞ control theory and linear matrix inequality techniques, a new approach for building vibration control over finite frequency range is presented. In comparison with the entire frequency control, the finite frequency approach proves much better performance in building vibration control over a certain frequency band in which strong earthquakes happen. A three-degree-of-freedom linear building structure under earthquake excitation is considered and simulations are employed to validate the effectiveness of the proposed approach in reducing seismic-excited building vibration.