Comments regarding "Stability margin evaluation for uncertain linear systems" [and counterexample]

The stability bound proposed in the above mentioned paper by Gong and Thompson (IEEE Trans. Automat. Contr. vol.39 (1994)) cannot be applied to all matrices having unstable unitary factor in their polar decompositions. The case study pursued in that paper and the succeeding papers is completed in this note in a rational way. Some basic results about the eigenvalues of unitary polar factor are also presented.