Using canonical models for LQR and H-infinity control of structures

According to the seismic modal approach, optimal modal control design should derive a control signal affecting only the dominant modal coordinates. However, existence of an optimal state feedback, affecting only a selected set of modes, is questionable. This study proves the existence of optimal modal feedback for the case of infinite horizon LQR and H∞ control methods. It defines a modal state space model by using a new state-space similarity transformation and solves the corresponding algebraic Riccati's equation. The solution is based on the selection of LQR weighting and H∞ output matrices. A modal design method is formulated and the spillover effect for the controlled structure is introduced.