Partial eigenvalue assignment problem of high order control systems using orthogonality relations

In this paper, we present an explicit solution to the partial eigenvalue assignment problem of high order control system using orthogonality relations between eigenvectors of the matrix polynomial. Our solution can be implemented with only a partial knowledge of the spectrum and the corresponding left eigenvectors of the matrix polynomial. We show that the number of eigenvalues and eigenvectors that need to remain unchanged will not affected by feedback. A numerical example is given to illustrate the applicability and the practical usefulness of the proposed method.