Defect correction method for the solution of algebraic Riccati equations

The solution of discrete and continuous algebraic Riccati equations is considered. It is shown that if an approximate solution is obtained, then the defect for this solution again solves an algebraic Riccati equation of the same form, and that the system properties of detectability and stabilizability are inherited by this defect equation. On the basis of these results, a general defect-correction method is proposed and numerical examples are given for the use of this method in combination with A. Bunse-Gerstner and V. Mehrmann´s (1986) SR method