Abstract: Based on the sliding-mode control and bang-bang control methods, a sliding-mode bang-bang control (SMBBC) method is presented in this paper. Since servohydraulic actuators are popular control-force delivery devices in actual structural control implementation, which are not suitable for high-speed switching of control-forces in bang-bang control, the modified sliding-mode bang-bang control (MSMBBC) law based on a smooth exponential function instead of sign function is investigated. Likewise, static output SMBBC that utilizes only the measured information from a limited number of sensors without an observer is also presented. Determination of maximum control-forces of actuators is investigated. The performance and robustness of the proposed control methods are studied in numerical simulation. The results demonstrate that the MSMBBC method is a viable and attractive control strategy for application to seismically excited linear structures.