Extended graphical representation of rational fractions with applications to cybernetics
type: Item
instance of: scholarly article
title: Extended graphical representation of rational fractions with applications to cybernetics
zbMATH Open document ID: 0607.65040
DOI: 10.1007/BF01875918
author: Chiaho Wong
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1981-01-01T00:00:00Z
review text: We discuss an extended graphical representation of the fraction of a complex variable s \(K=\sum^{n}_{i=0}a_ is^{n- i}/\sum^{m}_{j=0}b_ js^{m-j}\) where K is confined to be real. Three figures of the above fraction can be used in feedback systems as well as to study the properties of figures for anyone coefficient of a characteristic equation as a real parameter. It is easy to prove the following theorem: \[ K_ 1=f^{(n)}(s)/F^{(d)}(s)\quad and\quad K_ 2=F^{(d)}(s)/f^{(n)}(s) \] have the same root locus. By this graphical theory we find out that if the zeros and poles of a fraction are alternatively placed on the axis x, then there is no complex root locus of this fraction, therefore the state of such a system is always non-oscillatory. Using these figures of this fraction, we can discuss its stability interval systematically.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65S05
Mathematics Subject Classification ID: 93B55
zbMATH DE Number: 3982424
zbMATH Keywords: graphical representation
zbMATH Keywords: feedback systems
zbMATH Keywords: zeros
zbMATH Keywords: poles
zbMATH Keywords: fraction
zbMATH Keywords: interval
MaRDI profile type: Publication
cites work: Extended graphical representation of polynomials with applications to cybernetics
full work available at URL: https://doi.org/10.1007/bf01875918
OpenAlex ID: W2052717663
description: scientific article; zbMATH DE number 3982424