Asymmetric algebraic Riccati equation: A homeomorphic parametrization of the set of solutions

In this paper, asymmetric algebraic Riccati equations are analyzed. In particular, we derive a new parametrization of the set of solutions. Generalizing on the symmetric case, the proposed parametrization is obtained in terms of pairs of invariant subspaces of two related “feedback” matrices. Moreover, the connection is clarified between the new parametrization and the classical homeomorphic one based on graph invariant subspaces of the pseudo-Hamiltonian matrix associated with the equation. We finally show that also the newly introduced parametrization is given by a homeomorphic map.