Abstract
The structure of the set of hermitian solutions of the matrix quadratic equation $XDX - XA - A^ * X - C = 0$ is studied under the conditions that $C = C^ * $, D is positive semidefinite and $(A,D)$ is stabilizable. New features (e.g., nonexistence of the minimal solution) appear in contrast with the known case when $(A,D)$ is controllable.
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