This paper aims to study the effectiveness of using an active variable
damper system to control seismically excited building structures. The
Liapunov direct method was used to design the controller and the weig
hting matrix Q can be obtained by making the derivative of the Liapuno
v function as negative as possible. The control system, using an activ
e variable damper, provides time-varying damping to the structure at e
very instant of time and the error estimate of system matrix A will no
t significantly effect the control result. A comparison of the efficie
ncy of the control between classical optimal control and the present m
ethod is made, A combination of the active variable damper system with
a passive base-isolation system proved to be the most effective form
of control of the building response when subjected to seismic excitati
on even under different site conditions