A numerical method for computing the structured singular value
type: Item
instance of: scholarly article
title: A numerical method for computing the structured singular value
zbMATH Open document ID: 0653.65050
DOI: 10.1016/0167-6911(88)90035-7
author: J. William Helton
published in: Systems \& Control Letters
publication date: 1988-01-01T00:00:00Z
review text: The article is devoted to a numerical testing procedure for the robustness of systems whose performances can be expressed as \(\| F(z)\|\), where \(z\in M_{tr}\) contains uncertain parameters and for given matrices \(a\in M_{lk}\), \(b\in M_{lt}\), \(c\in M_{rk}\), \(d\in M_{rt}\), F is defined as \[ F_{\left( \begin{matrix} a\quad b\\ c\quad d\end{matrix} \right)}(z)=a+bz(I+dz)^{-1}c. \] The plant uncertainty problem is to verify if for given \(\left( \begin{matrix} a\quad b\\ c\quad d\end{matrix} \right)\) a simplex \(\Omega \subset M_{tr}\) and \(\rho >0\) the inequality \(\| F_{\left( \begin{matrix} a\quad b\\ c\quad d\end{matrix} \right)}(z)\| <\rho\) remains true for all \(z\in \Omega\). The proposed algorithm is based on transforming the initial problem in two subproblems: the first step is equivalent to a quadratic programming approach and the second needs to find the highest eigenvalue of a matrix.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 4066246
zbMATH Keywords: structured singular value
zbMATH Keywords: robust control
zbMATH Keywords: numerical optimization
zbMATH Keywords: plant uncertainty problem
zbMATH Keywords: quadratic programming
reviewed by: Octavian Pastravanu
MaRDI profile type: Publication
full work available at URL: 0167-6911(88)90035-7
OpenAlex ID: W1965440936
cites work: On the generalized numerical range
cites work: Characterization and efficient computation of the structured singular value
cites work: Exact calculation of the multiloop stability margin
cites work: Q3781601
cites work: Q4742652
description: scientific article; zbMATH DE number 4066246