Comments on "On the numerical solution of the discrete-time algebraic Riccati equation"

The problem discussed in the above paper has been independently considered by the authors in [1], [2]. The purpose of this note is to point out the differences with our approach of solving the same problem, to present a solution to the eigenvalue reordering problem which is left as work to be done in the paper, and to present an extension suitable for problems with singular loss matrix on control.