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Counterexamples in multidimensional system theory

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1 Author(s)
Jury, E.I. ; Dept. of Electrical Engng. & Computer Sci., Univ. of California, Berkeley, CA, USA

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.

Published in:

Circuits & Systems Magazine  (Volume:2 ,  Issue: 2 )