Stabilization of polynomially parametrized families of linear systems. The single-input case
type: Item
instance of: scholarly article
title: Stabilization of polynomially parametrized families of linear systems. The single-input case
zbMATH Open document ID: 0543.93052
DOI: 10.1016/0167-6911(83)90023-3
author: Richard T. Bumby
author: Eduardo D. Sontag
published in: Systems \& Control Letters
publication date: 1983-01-01T00:00:00Z
review text: The authors consider systems of the form \((1)\quad \dot x=A(p)x+b(p)u\) with n-dimensional state x and scalar control u. The matrix A and the vector b depend on an r-dimensional parameter p. Roughly speaking, the question is investigated of finding controls of the form \(u=k(p)x\) such that the closed-loop system is asymptotically stable, i.e. that the matrix \(A(p)+b(p)k(p)\) has all its eigenvalues in the left half plane. By using the Hurwitz stability test the authors show that the problem has a solution if and only if system (1) is controllable for each p. The treatment of this problem, which has also practical interest, is theoretic in nature. The well readable paper will be of interest primarily to those interested in various aspects of system theory.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 93B25
zbMATH DE Number: 3865108
zbMATH Keywords: families of systems
zbMATH Keywords: systems over rings
zbMATH Keywords: Hurwitz stability test
reviewed by: Inge Troch
MaRDI profile type: Publication
full work available at URL: 0167-6911(83)90023-3
OpenAlex ID: W2079484691
cites work: A nullstellensatz for ordered fields
cites work: Q5619178
cites work: On Necessary and Sufficient Conditions for Regulation of Linear Systems over Rings
cites work: Regulation of split linear systems over rings: Coefficient-assignment and observers
cites work: On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings
cites work: Ring models for delay-differential systems
description: scientific article; zbMATH DE number 3865108