On the number of invariant factors of partially prescribed matrices and control theory Original Research Article

Let A and B be matrices of sizes m×m and m×u, respectively, over an infinite field. Let i[A B] be the number of invariant factors of [xI−A −B] different from 1. This paper gives a necessary and sufficient condition for the existence of a matrix [A B], with a prescribed submatrix on the right lower corner, such that i[A B]less-than-or-equals, slantν. In particular, this paper studies the possibility of a linear system image being completely controllable, when a submatrix on the right lower corner of [A B] is unknown and all the other entries are prescribed.