The damping force of a damping force generation apparatus is controlled by operating an actuator on the basis of a control input u calculated by a state feedback controller K designed such that an L2 gain of a closed loop control system S which includes a generalized plant G designed by making use of a delay-approximated model M and the state feedback controller K therefor becomes less than a previously set positive constant γ. The delay-approximated model M is designed such that a delay element R representing operation delay of the actuator and a delay compensation element R* cancelling out the delay act on a mechanical motion model of the damping force generation apparatus. The delay-approximated model M is a bilinear system, and is designed to approximate a delay-considered model which is a control model designed on the basis of the mechanical motion model of the damping force generation apparatus and in consideration of the delay.