Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation
type: Item
instance of: scholarly article
title: Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation
zbMATH Open document ID: 0832.65042
DOI: 10.1016/0024-3795(93)00292-8
published in: Linear Algebra and its Applications
publication date: 1995-09-06T00:00:00Z
review text: The quadratic matrix equation \(X^2 - BX + C = 0\) is considered and its properties are emphasized. These properties are used to derive a new method for solving the algebraic Riccati equation (ARE). Then, using \textit{C. Van Loan's} idea [Linear Algebra Appl. 61, 233-251 (1984; Zbl 0565.65018)], an algorithm is given for the real ARE, consisting only of real operations and which takes account of special matrix structure. The advantages of the proposed algorithm are emphasized by applying it to some examples from a paper of \textit{A. J. Laub} [IEEE Trans. Autom. Control, AC-24, 913-921 (1979; Zbl 0424.65013)].
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 778239
zbMATH Keywords: Hamiltonian matrix
zbMATH Keywords: skew-Hamiltonian Schur form
zbMATH Keywords: quadratic matrix equation
zbMATH Keywords: algebraic Riccati equation
zbMATH Keywords: algorithm
author: Hongguo Xu
author: Linzhang Lu
reviewed by: Valeriu Prepeliţă
describes a project that uses: Algorithm 432
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)00292-8
OpenAlex ID: W1993854306
cites work: A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
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cites work: Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
cites work: Computing real square roots of a real matrix
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Wikidata QID: Q127975131
description: scientific article; zbMATH DE number 778239