Partial eigenvalue assignment of high order systems with time delay

An explicit solution to the partial eigenvalue assignment problem of high order control systems with time delay is presented. The problem is solved by a direct method without turning high order systems into the first order form. The solution can be implemented with only a partial knowledge of the eigenvalues and the corresponding eigenvectors of the matrix polynomial. Necessary and sufficient conditions for our results are proven. Numerical examples are given to illustrate the effect of the approach.