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Rational matrices: counting the poles and zeros

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4 Author(s)
Wyman, Bostwick F. ; Dept. of Math., Ohio State Univ., Columbus, OH, USA ; Sain, M.K. ; Conte, G. ; Perdon, A.-M.

The authors introduce finite-dimensional vector spaces which measure generic zeros which arise when a transfer function fails to be injective or subjective. An exact sequence relates the global spaces of zeros, the global spaces of poles, and the generic zero spaces. This sequence gives a structural result which can be described by the statement: the number of zeros of any transfer function is equal to the number of poles (when everything is counted appropriately). The same result unifies and extends a number of results of geometric control theory by relating global poles and zeros of general (possible improper) transfer functions to controlled invariant and controllability subspaces (including such spaces at infinity)

Published in:

Decision and Control, 1988., Proceedings of the 27th IEEE Conference on

Date of Conference:

7-9 Dec 1988