Title :
Counterexamples in multidimensional system theory
Author_Institution :
Dept. of Electrical Engng. & Computer Sci., Univ. of California, Berkeley, CA, USA
fDate :
6/1/1980 12:00:00 AM
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;
Journal_Title :
Circuits & Systems Magazine
DOI :
10.1109/MCAS.1980.6323681
