Discussion on: ``\((A,B)\)-invariance conditions of polyhedral domains for continuous-time systems'' by C. E. T. Dórea and J. -C. Hennet
type: Item
instance of: scholarly article
title: Discussion on: ``\((A,B)\)-invariance conditions of polyhedral domains for continuous-time systems'' by C. E. T. Dórea and J. -C. Hennet
zbMATH Open document ID: 0943.93019
DOI: 10.1016/S0947-3580(99)70142-1
published in: European Journal of Control
publication date: 2000-09-10T00:00:00Z
review text: As is clear from the title, this paper contains a discussion regarding the article of \textit{C. E. T. Dórea} and \textit{J.-C. Hennet} [Eur. J. Control 5, No. 1, 70-81 (1999; Zbl 0943.93018), see above]. Using the vertex representation of a polyhedral, the authors obtain dual equivalent conditions for this polyhedral to be \((A,B)\)-invariant. This result can be used to obtain equivalent conditions for \((A(t),B(t))\)-invariance of a polyhedral set, where \(A(t)\), \(B(t)\) are time-varying convex combination of some fixed matrices. Furthermore, the authors discuss the problems of infinite-directions, construction of the supremal \((A,B)\)-invariant set, and the feedback design. In the second section of this paper, Dórea and Hennet give their reaction on the new equivalent condition and the problems discussed in the first section.
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 1343404
zbMATH Keywords: \((A,B)\)-invariance
zbMATH Keywords: geometric theory
zbMATH Keywords: polyhedral set
zbMATH Keywords: positive invariance
zbMATH Keywords: vertex representation of a polyhedral set
author: Franco Blanchini
author: Stefano Miani
reviewed by: Hans Zwart
MaRDI profile type: Publication
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full work available at URL: s0947-3580(99)70142-1
OpenAlex ID: W1976936790
description: scientific article; zbMATH DE number 1343404