Real stability radii and quadratic matrix inequality
type: Item
instance of: scholarly article
title: Real stability radii and quadratic matrix inequality
zbMATH Open document ID: 0891.93063
author: O. Diekmann
published in: Chinese Science Bulletin
publication date: 1997-08-28T00:00:00Z
review text: A problem from robustness analysis is formulated as a parametric optimization problem. Consider the system \(dx/dt= (A+B\theta C)x\) with real matrices, and a fixed open set \(G\) in the complex plane. The system is said to be stable relative to \(G\) if \(G\) contains all eigenvalues of \(A\). Consider the matrix \(\theta\) as a parameter and denote its largest singular value by \(f^0(\theta)\). The authors consider the problem of minimizing \(f^0(\theta)\) so that the system is not \(G\)-stable. Under the linear constraint \(B=\theta A\), the problem reduces to \[ \inf_{\alpha>0} \{\alpha: \alpha^2 A^T A- B^TB\geq 0\}. \]
reviewed by: Sanjo Zlobec
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 1053792
zbMATH Keywords: robust stability
zbMATH Keywords: parametric optimization
zbMATH Keywords: singular value
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1053792