Recently semi-active control methods have been proposed and received much a
ttention. In semi-active base isolation. the coefficient of Viscous Jumping
or the spring constant are changed effectively according to the state of t
he control object. The system using a semi-active damper is classified as a
bilinear system which belongs to non-linear systems. In this paper, optima
l control theory is applied to a bilinear system using feedforward informat
ion of disturbance. and the bilinear optimal control law is derived. Then t
he method is applied to an actual building which is modelled by a 10 degree
-of-freedom structure model with base isolation using a semi-activce oil da
mper. The numerical analysis shows that the method has high control perform
ance in a wide frequency range, and it is effective for the vibration bare
isolation of building structures.