Unitary solutions of a class of algebraic Riccati equations and factorization

Abstract We consider the algebraic Riccati equation XD 1 X + XD 2 + D 3 X + D ∗ 1 = 0 , where D 2 and D 3 are self-adjoint. We are interested in contractive and unitary solutions X of this equation. Stability properties of such solutions under perturbations of the coefficients are studied. Further, the connection between unitary solutions of such equations and symmetric factorizations of nonnegative rational matrix functions is investigated.

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