Controllability completion problems of partial upper triangular matrices

The main result of this paper states sufficient conditions for the existence of a completion A(c) of an n x n partial upper triangular matrix A, such that the pair (A(c), B) has prescribed controllability indices, being B an n x m matrix. If A is a partial Hessenberg matrix some conditions may be dropped. An algorithm that obtains a completion A(c) of A such that pair (A(c), e(k)) is completely controllable, where ek is a unit vector, is used to proof the results.