An extension on a new formulation of the algebraic Riccati equation problem

In a recent paper [3], by utilizing the square root of a matrix approach a new formulation of the algebraic Riccati equation has been presented and a closed form solution has been obtained under the hypothesis that certain commutativity conditions are fulfilled on a transformed space. In this note the imposed conditions are weakened and the formulation is extended to a wider class of Riccati problems.