Equivalence Relations for the Algebraic Riccati Equation

Name: Equivalence Relations for the Algebraic Riccati Equation
Creator: Molinari, B. P.
Keywords: 0209 industrial biotechnology, 02 engineering and technology, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

Molinari, B. P.

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SIAM Journal on Control

Article . 1973 . Peer-reviewed

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https://dx.doi.org/10.1137/031...

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Equivalence Relations for the Algebraic Riccati Equation

Equivalence relations for the algebraic Riccati equation

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1973 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Control, volume 11, pages 272-285 (issn: 0036-1402,

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Authors: Molinari, B. P.;

doi: 10.1137/0311022

Equivalence Relations for the Algebraic Riccati Equation

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Abstract

By generalizing the notion of spectral factorization, solutions X of the matrix quadratic equation $BX + XA - XCDX + Q = 0$ are shown to have a one-to-one relation with factorizations of a rational matrix. By progressive specialization of this factorization, equivalence results are obtained in turn for symmetric solutions, Hermitian solutions, stabilizing solutions and positive definite solutions of the special case of the algebraic Riccati equation $F'X + XF - XGG'X + Q = 0$ .

Keywords

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

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