Partial eigenvalue assignment problems for time-delayed systems

In this paper, partial eigenvalue assignment problems for time-delayed systems are considered. A constructive method based on the orthogonality relations of quadratic pencil is provided. It is shown that it is possible to assign partial eigenvalues of a vibrating system while keeping the rest of the eigenvalues invariant in the presence of time delay provided that the original system is partial controllable for the eigenvalues that need to change. Specifically, the explicit solution for the single-input case and the parametric solution for the multi-input case are given.