Comments on "Upper matrix bounds for the discrete algebraic Riccati matrix equation" [with author\´s reply]

In the above paper (H. H. Choi, IEEE Trans. Automat. Contr., vol. 46, pp. 504-8, 2001), new methods to obtain upper matrix bounds for a discrete algebraic Riccati equation (DARE) have been established, but the author assumes that the system matrix A is nonsingular and DARE has a positive-definite solution. In this note, some similar results can be obtained when a solution is positive-semidefinite and there are no extra assumption that A is nonsingular. In reply the original author explains some of the underlying assumptions and comments on the computational burdens in the inequality in the commenters´ note.