On the Strong Solutions and Maximal Solutions of Generalized Algebraic Riccati Equations

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  • XIN Xin
    Department of Control and Systems Engineering, Tokyo Institute of Technology
  • MITA Tsutomu
    Department of Control and Systems Engineering, Tokyo Institute of Technology
  • HE Zhen
    Department of Control Engineering, Harbin Institute of Technology

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  • 一般化リカッチ方程式の強解と最大解について
  • イッパンカ リカッチ ホウテイシキ ノ キョウカイ ト サイダイカイ ニ ツイテ

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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.

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