Parametric stabilization is easy
type: Item
instance of: scholarly article
title: Parametric stabilization is easy
zbMATH Open document ID: 0548.93062
DOI: 10.1016/S0167-6911(84)80022-5
published in: Systems \& Control Letters
publication date: 1984-01-01T00:00:00Z
review text: This paper deals with parameter depending linear control systems of the form \(\dot x=A(\lambda)x+B(\lambda)u\) where the entries of the matrices \(A(\lambda)\), \(B(\lambda)\) are real polynomial functions of the parameter vector \(\lambda\in R^ r\). If the system is controllable for each \(\lambda\in R^ r\) and \(\gamma\) is an arbitrary real, it is shown that there exists a state feedback matrix \(K(\lambda)\) with entries polynomial in \(\lambda\) such that the spectrum of the closed loop matrix \(A(\lambda)+B(\lambda)K(\lambda)\) lies within the half plane [Re \(s\leq\gamma]\) for all \(\lambda\). This main result is illustrated by the computation of the feedback matrix \(K(\lambda)\) for an example with two state and two input variables, using the symbolic manipulation system REDUCE. It is shown that it is impossible to place the poles of the system arbitrarily by feedback matrices \(K(\lambda)\) which are continuous in \(\lambda\).
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C99
zbMATH DE Number: 3875100
zbMATH Keywords: systems over rings
zbMATH Keywords: parameter depending linear control systems
zbMATH Keywords: state feedback
reviewed by: D. Hinrichsen
MaRDI profile type: Publication
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full work available at URL: s0167-6911(84)80022-5
OpenAlex ID: W2011198266
author: Eduardo D. Sontag
description: scientific article; zbMATH DE number 3875100