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Plotting Robust Root Locus For Polynomial Families Of Multilinear Parameter Dependence Based On Zero Inclusion/Exclusion Tests
Author(s) -
Hwang Chyi,
Yang ShihFeng
Publication year - 2003
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2003.tb00120.x
Subject(s) - mathematics , multilinear map , zero (linguistics) , parametric statistics , polynomial , zero set , root locus , parametric equation , discrete mathematics , combinatorics , pure mathematics , mathematical analysis , geometry , statistics , philosophy , linguistics , electrical engineering , control system , engineering
The Mapping Theorem by Zadeh and Desoer [17] is a sufficient condition for the zero exclusion of the image or value set of an m ‐dimensional box B under a multilinear mapping f : R m → C , where R and C denote the real line and the complex plane, respectively. In this paper, we present a sufficient condition for the zero inclusion of the value set f (B). On the basis of these two conditions and the iterative subdivision of the box B , we propose a numerical procedure for testing whether or not the value set f (B) includes the origin. The procedure is easy to implement and is more efficient than that based on constructing the value set f (B) explicitly. As an application, the proposed zero inclusion test procedure is used along with a homotopy continuation algorithm to trace out the boundary curves of the robust root loci of polynomial families with multilinear parametric uncertainties.