A vibration control scheme for buildings with a magnetorheological damper is presented. For a building shear model, an adaptive observer is designed to recover position and velocity signals and the parameters of each story of the building and a control law is designed for the damper via Lyapunov analysis. The main contribution is the combined stability analysis of the controller-observer system. The strategy is tested through simulations with the seismic record of Santiago, Chile 1985. Very good levels of attenuation are attained.

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