Perturbation bounds for coupled matrix Riccati equations
type: Item
instance of: scholarly article
title: Perturbation bounds for coupled matrix Riccati equations
zbMATH Open document ID: 1017.15006
DOI: 10.1016/S0024-3795(02)00416-0
author: V. A. Angelova
author: Mihail M. Konstantinov
author: Petko Hr. Petkov
author: Da-Wei Gu
author: Vassilios A. Tsachouridis
published in: Linear Algebra and its Applications
publication date: 2003-03-23T00:00:00Z
review text: The paper presents a complete local and non-local perturbation analysis of the real continuous-time coupled algebraic matrix Riccati equations (CCAREs) of the form \(F_{i}(X_{1},X_{2},P_{i})=0,i=1,2\) where \(F_{i}\) are matrix quadratic functions in the unknown matrices \(X_{i}\), and \(P_{i}\) are collection of matrix coefficients. CCAREs of this type arise naturally in \( H_{2}/H_{\infty }\) analysis and design of linear control systems. The techniques that have been used are the Lyapunov majorants and fixed point principles. Finally, an experimental analysis is made to compare the performance of the proposed perturbation bounds. The techniques for the perturbation analysis, as well as the perturbation bounds that have been derived, may be extended to other more general systems of matrix quadratic equations.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 1886837
zbMATH Keywords: perturbation analysis
zbMATH Keywords: coupled algebraic matrix Riccati equations
zbMATH Keywords: condition numbers
zbMATH Keywords: \(H_{2}/H_{\infty }\) control
zbMATH Keywords: Lyapunov majorants
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1886837