Stabilizability of multivariable systems and the Ljusternik-Snirel'mann category of real Grassmannians
type: Item
instance of: scholarly article
title: Stabilizability of multivariable systems and the Ljusternik-Snirel'mann category of real Grassmannians
zbMATH Open document ID: 0554.93055
DOI: 10.1016/0167-6911(83)90024-5
author: C. I. Byrnes
published in: Systems \& Control Letters
publication date: 1983-01-01T00:00:00Z
review text: The problem of stabilization (or, more generally, pole-shifting) by static output feedback has attracted a considerable amount of nontrivial and very nice mathematics, of which this paper is an example. The goal is to find the function, say b(m,p), such that b(m,p) is the largest integer n for which it is known that (generically) systems of dimension n and m inputs, p outputs, can be stabilized. It is known that \(mp\geq b(m,p)\geq m+p\)-1, but very little else in that generality. Based on algebraic geometric calculations, better (but difficult to calculate) bounds are given in this paper. For example, it is shown as a corollary of more general results, that b(2,6)\(\geq 9\).
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 3884057
zbMATH Keywords: pole-shifting
zbMATH Keywords: static output feedback
MaRDI profile type: Publication
full work available at URL: 0167-6911(83)90024-5
OpenAlex ID: W2013422403
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description: scientific article; zbMATH DE number 3884057