This paper proposes control for a seismically excited N story building. Intrinsic properties of the building's own robustness are analyzed by using an input‐to‐state stability method and solving a linear matrix inequality. Then frequency analysis on the base isolation gives guidelines for choosing parameters and also reveals the narrow flexibility of the base parameters. This frequency analysis, on the other hand, shows the need for a hybrid controller. Therefore a passive baseisolated building model is considered with an active hydraulic actuator. This passive and active combined hybrid controller is then designed using the backsteppping approach. The parametric uncertainties of both the building and the actuator are considered. Therefore an adaptive backstepping controller is designed. An H8 criterion is given to attenuate the effects of seismic excitation. Numerical simulations are carried out using the Chi‐Chi earthquake of Taiwan as an excitation source on a twelve story building. Results show that the hybrid system design is valid, with reasonable control force.
Journal of the Chinese Institute of Engineers=中國工程學刊 25(4), pp.403-414