All solutions to the positive real version of the Parrott´s problem

In this paper, a new formula for all solutions Q to the matrix inequality problem herm{R+UQV^T}>0 is derived. The derivation does not involve a bilinear sector transformation of the Parrott´s theorem, and leads to a parameterization of all solutions Q with only one free matrix as opposed to several matrices given in Gabinet et al. (1994) and Iwasaki et al. (1994). The other favorable property of our result is that the expression for all solutions is computationally less costly due to fewer square root and inverse operations involving lower dimensioned matrices compared to previously reported results