Existence condition of positive-definite solutions for algebraic matrix Riccati equations
type: Item
instance of: scholarly article
title: Existence condition of positive-definite solutions for algebraic matrix Riccati equations
zbMATH Open document ID: 0616.93021
DOI: 10.1016/0005-1098(87)90013-6
author: Hiroyuki Kano
published in: Automatica
publication date: 1987-01-01T00:00:00Z
review text: Algebraic matrix Riccati equations are considered which arise in the optimal filtering as well as in control problems of continuous time-invariant systems. A necessary and sufficient condition is established for the existence of unique positive-definite solutions and the asymptotically stable closed-loop system. The condition is stated in terms of the detectability and stabilizability of certain matrix pairs, as was the case for the non-negative-definite solution. Simple examples are included to illustrate the new results against the existing ones.
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 3999759
zbMATH Keywords: Algebraic matrix Riccati equations
zbMATH Keywords: optimal filtering
zbMATH Keywords: existence of unique positive-definite solutions
zbMATH Keywords: asymptotically stable closed-loop system
zbMATH Keywords: detectability
zbMATH Keywords: stabilizability
MaRDI profile type: Publication
full work available at URL: 0005-1098(87)90013-6
OpenAlex ID: W2051803526
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description: scientific article; zbMATH DE number 3999759