Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term
zbMATH Open document ID: 0754.34065
DOI: 10.1007/BF01218397
published in: Applied Mathematics and Optimization
publication date: 1993-01-16T00:00:00Z
review text: The author gives necessary and sufficient conditions for existence of positive definite and negative definite solutions to algebraic Riccati equations. He gives examples of optimization problems in game and control theory giving rise to these equations. He gives explicit formulas for solutions and also a quadratically converging iterative algorithm. His methods include integral transforms and retranslating the problem into control theory.
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 92898
zbMATH Keywords: linear quadratic control problem
zbMATH Keywords: two-person zero-sum differential game
zbMATH Keywords: \(H^ \infty\)-optimization
zbMATH Keywords: positive definite and negative definite solutions
zbMATH Keywords: algebraic Riccati equations
zbMATH Keywords: optimization problems
zbMATH Keywords: iterative algorithm
zbMATH Keywords: integral transforms
author: Shuping Chen
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
cites work: Q5752866
cites work: State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
cites work: Values and strategies for infinite time linear quadratic games
cites work: Matrix Quadratic Solutions
cites work: The Regular Free-Endpoint Linear Quadratic Problem with Indefinite Cost
cites work: An algebraic Riccati equation approach to \(H^{\infty}\) optimization
full work available at URL: https://doi.org/10.1007/bf01218397
OpenAlex ID: W1977068734
description: scientific article; zbMATH DE number 92898