Residual bounds of approximate solutions of the discrete-time algebraic Riccati equation
type: Item
instance of: scholarly article
title: Residual bounds of approximate solutions of the discrete-time algebraic Riccati equation
zbMATH Open document ID: 0888.65051
author: Ji-guang Sun
published in: Numerische Mathematik
publication date: 1998-02-01T00:00:00Z
review text: Perturbation theory is investigated for the discrete-time algebraic Riccati equation which arises in the solution of quadratic optimization and estimation problems in linear control theory. The main contribution of the paper is to derive residual bounds for the approximate solution. Firstly one studies stable matrices. Then one derives a perturbation equation which contains the residual of the Riccati equation w.r.t. the approximate Hermitian solution. Bounds for the approximate solution are obtained. A numerical example is displayed.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 1111585
zbMATH Keywords: error bounds
zbMATH Keywords: perturbation theory
zbMATH Keywords: discrete-time algebraic Riccati equation
zbMATH Keywords: quadratic optimization
zbMATH Keywords: linear control theory
zbMATH Keywords: approximate Hermitian solution
zbMATH Keywords: numerical example
reviewed by: Guy Jumarie
MaRDI profile type: Publication
full work available at URL: s002110050321
OpenAlex ID: W2067914565
DOI: 10.1007/S002110050321
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description: scientific article; zbMATH DE number 1111585