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This paper develops a robust observer for a class of linear systems subject to unknown signals, uncertainties, and disturbance output measurements for building structure systems. The highlight of the proposed observer is that it mitigates the adverse effects present in physical systems as it happens with the structural systems of buildings. The proposed robust observer provides a simultaneous estimation of building displacements and velocities (state vector) and the seismic force acceleration signal (unknown input) from noisy acceleration measurements of the structure. These estimations can help to reduce the displacements of building structure systems with the aid of a vibration controller. The convergence analysis of the proposed robust observer is based on Lyapunov theory, which resulted in a simple set of Linear Matrix Inequalities. An example considering a two-story building-like structure was performed to …