Abstract: Due to the excessive number of degrees of freedom in actual building structures, controller design and real-time execution become challenging. Model order reduction is an effective approach to reduce model complexity while satisfying the engineering accuracy requirements. The degree of matching between the reduced-order model and the full-order model significantly affects the control performance of the reduced-order controller. Addressing the challenges posed by parameter uncertainty and model uncertainty resulting from model reduction is crucial for maintaining system performance. This study proposes a multi-objective optimization robust control algorithm by the grounds of the reduced-order controller and, of utilizing robust H₂/H_∞ optimal guaranteed cost control (OGCC) theory and of the linear matrix inequality (LMI) method. Based on the reduced-order model with uncertainty, the necessary and sufficient conditions for the existence of the proposed OGCC are established and proved. By introducing a deterministic H₂ performance upper bound, the controller design problem is transformed into a standard convex optimization problem with LMI constraints, facilitating the solution process. Using the finite element software ABAQUS as the simulation platform, the effectiveness of the proposed algorithm is tested by a real engineering case of lateral-torsional coupled wind vibration control for a super high-rise building with a large length-width ratio. The results indicate that the OGCC algorithm proposed significantly outperforms the LQR control algorithm upon the nominal model and has stronger robustness for model uncertainty and parameter uncertainty.