Canonical matrix factorisation and polynomial Riccati equations
type: Item
instance of: scholarly article
title: Canonical matrix factorisation and polynomial Riccati equations
zbMATH Open document ID: 0880.93010
DOI: 10.1016/S0947-3580(97)70061-X
author: A. E. Barabanov
published in: European Journal of Control
publication date: 1998-02-10T00:00:00Z
review text: Let \(R(z)\) be a symmetric \(n\times n\) polynomial matrix, and let \(\mu= (M_1, \dots, M_n)\), \(M_k\) being positive integers. A \(\mu\)-factorization of \(R(z)\) means writing \(R(z)= \Pi^*(z) C\Pi(z)\), where the \(k\)th column of \(\Pi(z)\) has degree at most \(M_k\). The main results state that: a) The successive factor extraction algorithm adapted to \(\mu\)-factorization does always find a solution if it exists. b) Existence of a \(\mu\)-factorization is equivalent to the existence of a solution to a corresponding polynomial Riccati equation. c) For any minimal state-space realization the existence of a \(\mu\)-factorization is equivalent to the existence of an antistabilising solution of the adjoined Riccati equation. d) A criterion for existence of a \(\mu\)-factorizaion is expressed in terms of poles of the matrix \(R(z)^{-1}\).
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 1057557
zbMATH Keywords: \(\mu\)-factorization
zbMATH Keywords: polynomial matrix
zbMATH Keywords: polynomial Riccati equation
MaRDI profile type: Publication
cites work: Optimization by frequency-uniform criteria (\(H\)-theory)
cites work: Q4370793
cites work: On polynomial matrix spectral factorization by symmetric extraction
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: Q3335637
cites work: Factorization of selfadjoint matrix polynomials with constant signature
cites work: Minimax frequency domain performance and robustness optimization of linear feedback systems
cites work: Q4028752
cites work: Polynomial J-spectral factorization
cites work: Q5521804
cites work: Q5680247
description: scientific article; zbMATH DE number 1057557