On the strong solutions of generalized algebraic Riccati equations

Abstract

A comparison theorem for the solutions of two generalized algebraic Riccati equations (GAREs) coming from two different systems is presented. It is then shown that the so-called strong solutions, whose related pencils have all their the finite eigenvalues in the closed left half plane, are maximal. The results obtained generalize the existing monotonicity results of algebraic Riccati equations. An application of the results is the derivation of the parameterization of all strong solutions to the GARE related to the singular spectral factorization of a proper transfer function with finite and infinite imaginary axis zeros.