On the relationship between controllability indexes, Eigenvector assignment, and deadbeat control

The subspaces, to which closed-loop generalized eigenvectors are restricted, are described in terms of the controllability indexes of the pair (
A, B
) and the polynomials of minimal degree that span ker[
A- \lambda I, B
]. This characterization of the eigenspaces is then used to calculate the deadbeat controller of minimum Frobenius norm.