To mitigate seismic responses of buildings under earthquake excitation, this study considers actuator force constraints and proposes an active control methodology ensuring H∞ performance. First, sensors are deployed on building floors to capture relative displacement and velocity signals. Seismic excitation is characterized as energy-bounded uncontrollable disturbances. Based on this framework, a controllable building model is established. Subsequently, damper output force constraints are transformed into a saturation control problem with actuator force amplitude limiting, forming the basis for the development of an active seismic control controller. Finally, through Lyapunov stability analysis, a controller synthesis method simultaneously ensuring saturation constraints and H∞ performance is derived. Simulated results demonstrate that deploying two actuators, each with a maximum output of 6 kN, at the top and sub-top floors of an 11-story building leads to a reduction of approximately 45% in structural displacement and velocity responses under El-Centro earthquake excitation. These findings validate the effectiveness of the proposed approach.