In this paper, we consider the partial quadratic eigenvalue assignment problem (PQEAP) for vibration system by active feedback control, such that some "troublesome" eigenpairs are replaced by some suitable chosen or newly measured ones, while the remaining unknown eigenpairs are kept unchanged. With the assumptions that the mass and stiffness matrices are nonsingular, we give a new proof of the spectral decomposition of quadratic symmetric pencil. And then we provide some necessary and sufficient conditions of the feedback matrices so that the closed-loop can preserve the no spill-over propert...
