Controllability and stability radii for companion form systems
type: Item
instance of: scholarly article
title: Controllability and stability radii for companion form systems
zbMATH Open document ID: 0657.93007
DOI: 10.1007/BF02551286
author: Alan J. Laub
author: Charles S. Kenney
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1988-01-01T00:00:00Z
review text: The paper unites and extends earlier work on robustness measures for the controllability, stabilizability and stability of finite-dimensional linear state-space systems [cf., \textit{R. Eising}, Syst. Control Lett. 4, 263-264 (1984; Zbl 0542.93007); \textit{C. F. Van Loan}, Contemp. Math. 47, 465-478 (1985; Zbl 0576.15011); \textit{D. Hinrichsen} and \textit{A. J. Pritchard}, Syst. Control Lett. 7, 1-10 (1986; Zbl 0631.93064)]. By deriving simple formulas for the singular values of companion form matrices, the authors are able to bound these robustness measures for systems which are in controllable canonical form. As a result it is shown for example, that almost all high-order controllable canonical forms are nearly uncontrollable. This supports earlier empirical observations that high-order companion system models have certain undesirable numerical properties.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 4074884
zbMATH Keywords: robustness measures
zbMATH Keywords: controllability
zbMATH Keywords: stabilizability
zbMATH Keywords: finite-dimensional linear state-space systems
zbMATH Keywords: singular values
zbMATH Keywords: companion form matrices
reviewed by: H. Logemann
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02551286
OpenAlex ID: W1981482844
description: scientific article; zbMATH DE number 4074884