Minimum norm partial eigenvalue assignment of high order linear system with no spill-over

In this paper, we consider the partial eigenvalue assignment problem (PEAP) of high order linear system by state feedback. To prevent spill-over phenomenon, we establish the new orthogonality relations for the eigenvectors of matrix polynomial such that the unwanted eigenvalues are moved to prescribed values and the wanted eigenvalues remain unchanged. Based on the orthogonality relations, the solvability conditions for PEAP are presented and the parametric expression of feedback matrices is derived in terms of the known quantities only. Finally, an optimization-based algorithm is proposed to find the minimum norm solution. Two numerical examples are given to show the application of the proposed method.