Abstract: Based on the combination of sliding-mode control(SMC) and bang-bang control(BBC),a discrete sliding-mode bang-bang control(DSMBBC) method is proposed in this paper.Since actuators applied in the system are not suitable for the high-speed switching of positive and negative maximum control-forces in the DSMBBC case,a modified discrete sliding-mode bang-bang control(MDSMBBC) method is presented.In consideration of the actuators' unnecessary continuous exertion of control-forces on the structure in the whole process of earthquake,a conditional discrete sliding-mode bang-bang control(CDMSMBBC) method is presented too.In addition,the determination method of maximum control-force of actuator is discussed through numerical computation.The performance and robustness of the control methods are all demonstrated by numerical simulations.Simulation results indicate that the control effectiveness of the proposed methods is remarkable in reducing maximum responses of the structure in comparison with that of the discrete LQR method,and is robust with respect to system parametric uncertainties as well.