On the Strong Solutions and Maximal 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 in this paper. It is then shown that the so-called strong solutions, whose related pencils have all their finite eigenvalues in the closed left half plane, are maximal. The results obtained in this paper generalize the existing monotonicity results of algebraic Riccati equations. An application of the results is the derivation of the parameterization of all strong solutions of the GARE related to the singular spectral factorization of a proper transfer function with finite and infinite imaginary axis zeros.