Abstract: An output feedback H_∞ guaranteed cost robust decentralized control algorithm is proposed here for dealing with the influence of the parameter uncertainties of a building structure, which can meet the requirements of multiple control objectives simultaneously. Based on Lyapunov stability theory and LMI method, the sufficient conditions for the existence of a robust H_∞ guaranteed cost decentralized controller is developed and proved. Then the output feedback H_∞ guaranteed cost robust decentralized control algorithm is established by using a variable substitution method. Furthermore, by introducing the constraint conditions, the H_∞ guaranteed cost robust controller design is transformed into a convex optimization problem with linear matrix inequality constraints. A 12-story building is selected as a numerical example to illustrate the control performances of the proposed decentralized algorithm. Numerical simulation results indicate that for the building structure with large uncertain parameters, the proposed output feedback H_∞ guaranteed cost robust decentralized control algorithm has better control effect than that of traditional LQG centralized control algorithm.