Multi-input partial eigenvalue assignment for the symmetric quadratic pencil

A new algorithm is proposed for the multi-input partial pole placement problem by the state feedback for a quadratic pencil. A set of necessary and sufficient conditions for the existence of a solution is also derived. The important features of the algorithm are that the algorithm requires knowledge of only a small number of the eigenvalues that need to be re-assigned in practice and does not give any spill-over, that is, the eigenvalues that are not required to be changed, remain unchanged. Furthermore, it can take advantage of the exploitable structures of the system matrices such as the sparsity, symmetry and definiteness. The solution may be of particular interest in the stabilization and control of flexible, large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum has to remain unchanged.