DocumentCode
836818
Title
A general theory for matrix root-clustering in subregions of the complex plane
Author
Gutman, Shaul ; Jury, Eliahu I.
Author_Institution
Technion-Israel Institute of Technology, Haifa, Israel
Volume
26
Issue
4
fYear
1981
fDate
8/1/1981 12:00:00 AM
Firstpage
853
Lastpage
863
Abstract
We consider the general problem of root-clustering of a matrix in the complex plane: Let 
and 
. Find the largest class of 
and an algebraic criterion which is necessary and sufficient for ![\\lambda _{i}[A] \\in S, i=1,2,..., n](/images/tex/3666.gif)
. We introduce two types of regions which constitute the largest class of known to date. The criterion is presented both for open regions and closed ones. The results are used to define a design methodology for control systems. Moreover, all classical results are shown to be special cases of the present theory.
and . Find the largest class of and an algebraic criterion which is necessary and sufficient for . We introduce two types of regions which constitute the largest class of known to date. The criterion is presented both for open regions and closed ones. The results are used to define a design methodology for control systems. Moreover, all classical results are shown to be special cases of the present theory.Keywords
Matrices; Poles and zeros; Asymptotic stability; Control systems; Design methodology; Difference equations; Differential equations; Eigenvalues and eigenfunctions; Helium; Linear matrix inequalities; Linear systems; Polynomials;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1981.1102764
Filename
1102764
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