ON FEEDBACK EQUIVALENCE AND COMPLETION PROBLEMS

In 1987, I. Zaballa characterized the possible similarity classes of a square matrix with some prescribed rows. In 1988, the same author cha racterized the possible feedback equivalence classes of [A B], where A is a fixed square matrix and B varies. Firstly, in this paper, we obs erve that these results are equivalent, that is, each one of them can be obtained as a corollary of the other. Then, we apply similar argume nts to other inverse problems. In particular, we study the possible in variant polynomials and the possible characteristic polynomials of A EX + YC, when X and Y vary, and we study the linear systems that can become completely observable with a suitable choice of linear state fe edback control. (C) 1997 Elsevier Science Inc.