Linear second-order matrix systems representing dynamics of large flexible structures are recast in a state space form. By can efficient partial decoupling technique, a few of low frequency modes are decoupled from the rest of modes, and an optimal control procedure is developed in such a way that damping is added to the selected modes without control spillover to uncontrolled modes. Since the partial decoupling requires only eigenvectors of the sected modes, the computing time can be reduced significantly in large systems. Therefore, the method of partial decoupling and control developed in this work may be applicable to vibration contorl of large flexible space structures.