Alternative derivation of the algebraic Riccati equation in \(\mathcal{H}_ \infty\) control
type: Item
instance of: scholarly article
title: Alternative derivation of the algebraic Riccati equation in \(\mathcal{H}_ \infty\) control
zbMATH Open document ID: 0870.93012
DOI: 10.1016/S0005-1098(96)00131-8
author: Kazunobu Kuriyama
author: Tsutomu Mita
published in: Automatica
publication date: 1997-08-04T00:00:00Z
review text: The full-information \(H_\infty\)-control problem for finite-dimensional linear, time-invariant, continuous-time systems is considered. The well-known solution to the problem is described by the use of algebraic Riccati equations. The purpose of the paper, originally written for students, is to present an alternative proof of the Riccati equation condition obtained by \textit{J. C. Doyle, K. Glover, P. P. Khargonekar} and \textit{B. A. Francis} [IEEE Trans. Autom. Control 34, No. 8, 831-847 (1989; Zbl 0698.93031)]. The given derivation is based on the standard techniques developed for linear control problems formulated in the frequency domain. The paper seems to be helpful, and not only for purely tutorial purposes.
reviewed by: O. I. Nikonov
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93-01
zbMATH DE Number: 987793
zbMATH Keywords: full-information
zbMATH Keywords: \(H_ \infty\)-control
zbMATH Keywords: linear
zbMATH Keywords: time-invariant
zbMATH Keywords: continuous-time
zbMATH Keywords: algebraic Riccati equations
zbMATH Keywords: alternative proof
MaRDI profile type: Publication
cites work: State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
cites work: A course in \(H_{\infty}\) control theory
cites work: State-space formulae for all stabilizing controllers that satisfy an \(H_{\infty}\)-norm bound and relations to risk sensitivity
cites work: A Characterization of All Solutions to the Four Block General Distance Problem
cites work: A contribution to matrix quadratic equations
cites work: Simplifying theH∞ theory via loop-shifting, matrix-pencil and descriptor concepts
cites work: Solution to the positive real control problem for linear time-invariant systems
cites work: Q3751436
Recommended article: Reduced-order \(H^\infty\) controller design -- an algebraic Riccati equation approach
Recommended article: Q5482750
Recommended article: An algebraic approach to \(H_{\infty}\) output feedback control problems
Recommended article: Analytic feedback control and the algebraic Riccati equation
Recommended article: Algebraic Riccati Equation Arising in Boundary Control Problems
Recommended article: New iterative algorithm for algebraic Riccati equation related to H/sub ∞/ control problem of singularly perturbed systems
Recommended article: Q4362955
Recommended article: Stabilizing solutions of the \(H_ \infty\) algebraic Riccati equation
Recommended article: Q4460201
description: scientific article; zbMATH DE number 987793