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This paper investigates solutions X of the algebraic Riccati equation $F'X + XF - XGG'X + Q = 0$ with the property Re λ (F - GG' X) 0. The uniqueness and existence of such a solution is completely characterized. In addition, the conditions are strengthened to characterize the important stabilizing solution (Re λ (F - GG' X) < 0). All standard existence results are recovered as special cases.
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B. Molinari (1973) studied this question.
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