Equivalence Relations for the Algebraic Riccati Equation
B. Molinari · SIAM Journal on Control · 1973
By generalizing the notion of spectral factorization, solutions X of the matrix quadratic equation $BX + XA - XCDX + Q = 0$ are shown to have a one-to-one relation with factorizations of a rational matrix. By progressive specialization of this factorization, equivalence results are obtained in turn for symmetric solutions, Hermitian solutions, stabilizing solutions and positive definite solutions of the special case of the algebraic Riccati equation $F'X + XF - XGG'X + Q = 0$ .