On computing the stabilizing solution of the discrete-time Riccati equation
type: Item
instance of: scholarly article
title: On computing the stabilizing solution of the discrete-time Riccati equation
zbMATH Open document ID: 0756.15020
DOI: 10.1016/0024-3795(92)90053-D
author: Vlad Ionescu
author: Martin Weiss
published in: Linear Algebra and its Applications
publication date: 1992-10-26T00:00:00Z
review text: The discrete-time Riccati equation (DTARE) is \[ A^ TXA-X-(L+A^ TXB)(R+B^ TXB)^{-1}(B^ TXA+L^ T)+Q=0, \] where \(A\in\mathbb{R}^{n\times n}\), \(B\in\mathbb{R}^{n\times m}\), \(R=R^ T\in\mathbb{R}^{m\times m}\), \(L\in\mathbb{R}^{n\times m}\), and \(Q=Q^ T\in\mathbb{R}^{n\times n}\). The matrix \(X=X^ T\in\mathbb{R}^{n\times n}\) is said to be a stabilizing solution of the DTARE if \(R+B^ TXB\) is invertible. A necessary and sufficient condition for the existence of a stabilizing solution is given which does not include invertibility or positivity assumptions. The result involves a special associated matrix pencil. An algorithm and a numerical example are given.
reviewed by: D. Kershaw
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 69531
zbMATH Keywords: discrete-time Riccati equation
zbMATH Keywords: stabilizing solution
zbMATH Keywords: matrix pencil
zbMATH Keywords: algorithm
zbMATH Keywords: numerical example
describes a project that uses: HTools
MaRDI profile type: Publication
cites work: Q4401802
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cites work: Comments on "On the numerical solution of the discrete-time algebraic Riccati equation"
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description: scientific article; zbMATH DE number 69531