How to decompose semi-definite discrete-time algebraic Riccati equations
type: Item
instance of: scholarly article
title: How to decompose semi-definite discrete-time algebraic Riccati equations
zbMATH Open document ID: 0934.93042
DOI: 10.1016/S0947-3580(99)70159-7
author: Yanyan Li
published in: European Journal of Control
publication date: 2000-04-04T00:00:00Z
review text: Interest in the algebraic Riccati equation (ARE) was revived by the theory of \(H^\infty\) control. In this case the weight matrix in the performance index is not positive definite but usually indefinite. Even the case when the weight matrix is positive semi-definite, which is the case in standard \(H^\infty\) control, was not fully understood, and the question of how to implement good numerical solvers for these equations when they are ill posed is still a research area. The aim of the paper is to propose a way of circumventing the problems of today's numerical solvers for the semi-definite case. The idea is to decompose the potentially ill-posed equation into a trivial part and a reduced-order well-posed equation that can be solved in a numerically stable and efficient way by well-known solvers such as the Schur method or the Newton method. The proposed reduction scheme is designed for the discrete-time ARE (DARE). As a by-product a novel constructive proof for the existence of a solution to the DARE is obtained. The reduction scheme is implemented in Matlab, and it is shown in several examples that the new scheme is very promising.
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 49N10
zbMATH DE Number: 1382825
zbMATH Keywords: algebraic Riccati equations
zbMATH Keywords: discrete-time systems
zbMATH Keywords: condition numbers
zbMATH Keywords: decomposition methods
zbMATH Keywords: Kalman filters
zbMATH Keywords: linear quadratic regulators
zbMATH Keywords: transfer function zeros
zbMATH Keywords: ill-posedness
zbMATH Keywords: reduction schemes
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: indefinite weights
describes a project that uses: RICPAC
describes a project that uses: LAPACK
describes a project that uses: mexFunction
describes a project that uses: MEX-file
describes a project that uses: Matlab
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1382825