Abstract
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 weighting matrix Q can be obtained by making the derivative of the Liapunov function as negative as possible. The control system, using an active variable damper, provides time-varying damping to the structure at every instant of time and the error estimate of system matrix A will not significantly effect the control result. A comparison of the efficiency of the control between classical optimal control and the present method 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 excitation even under different site conditions
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