Existence and uniqueness theorems for the algebraic Riccati equation
Peter Lancaster, Leiba Rodman · International Journal of Control · 1980
Necessary and sufficient conditions for existence and uniqueness of hermitian solutions of the algebraic n×n matrix Riccati equation (D≥0,C∗=C,(A, D) controllable) are obtained. The conditions are formulated in terms of the spectral structure of a certain 2n × 2n matrix. A description is also given of the set of solutions in a geometrical language of invariant subspaces which are neutral with respect to a certain indefinite scalar product. This technique is then applied to provide some results on existence and uniqueness of solutions which are not necessarily hermitian. The problem is also approached (when Dz;> 0)via a related unilateral equation. for Z where K1 ∗ equals K1, K0 ∗ equals K0