Unitary solutions of a class of algebraic Riccati equations and factorization (Q1183204)

This paper considers the algebraic Riccati equation \(XD_ 1X+XD_ 2+D_ 3X+D^*_ 1=0\) where \(D_ 2\) and \(D_ 3\) are self-adjoint. Contractive and unitary solutions are characterized using angular subspaces. Stability properties of such solutions under perturbations of the coefficients are studied. The connection between unitary solutions of such Riccati equations and symmetric factorizations of nonnegative rational matrix functions is investigated. Some of the results assume finite dimensionality.