A state observer for a building with a magneto-rheological damper and parameter uncertainty

A real-time parameters and state estimation scheme for a shear multi-degree-of-freedom building with a magneto-rheological damper is presented. The design follows standard Lyapunov's theory and exploits the bilinear structure of the mathematical model of the building to construct the adaptation law for the parameters and the observer for the model states. A sufficient condition for stability is given via a linear matrix inequality. The design is illustrated simulations of a small scale three-story building subject to seismic excitation. Results indicate that the observer is able to recover system's state and parameters by using only measurements of the stories acceleration