Structured perturbation of the Brunovsky form: A particular case

We study the variation of the feedback invariants of a complex rectangular n×(n+m) matrix when we make small additive perturbations on the last m columns, in the particular case when the square n×n submatrix is similar to a block diagonal matrix, with two blocks in the diagonal associated with the controllable part and the noncontrollable part of the pair (A,B), respectively.