DocumentCode
1309184
Title
Counterexamples in multidimensional system theory
Author
Jury, E.I.
Author_Institution
Dept. of Electrical Engng. & Computer Sci., Univ. of California, Berkeley, CA, USA
Volume
2
Issue
2
fYear
1980
fDate
6/1/1980 12:00:00 AM
Firstpage
1
Lastpage
4
Abstract
In extending some of the basic concepts of one dimensional system theory to two and multidimensional systems one encounters many difficulties. Discussion of such extension is reviewed and several counterexamples are given. In particular counterexamples to least square inverse polynomials, discrete Hilbert transform, bilinear transformation, necessary and sufficient conditions for linear time-invariant stability, primitive factorization for higher than two dimensional polynomial matrices and partial fraction expansion are given. Furthermore, several conjectures regarding the validity for such extensions are discussed.
Keywords
least squares approximations; multidimensional systems; stability; transforms; bilinear transformation; discrete Hilbert transform; least square inverse polynomials; linear time invariant stability; multidimensional system theory; partial fraction expansion; primitive factorisation; Circuit stability; Digital filters; Educational institutions; Multidimensional systems; Polynomials; Transforms;
fLanguage
English
Journal_Title
Circuits & Systems Magazine
Publisher
ieee
ISSN
0163-6812
Type
jour
DOI
10.1109/MCAS.1980.6323681
Filename
6323681
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