Rational matrices: counting the poles and zeros

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...

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Bibliographic Details
Published inProceedings of the 27th IEEE Conference on Decision and Control pp. 921 - 925 vol.2
Main Authors Wyman, B.F., Sain, M.K., Conte, G., Perdon, A.-M.
Format Conference Proceeding
LanguageEnglish
Published IEEE 1988
Subjects
Control theory
Feedback
Filtering theory
H infinity control
Linear systems
Mathematics
Poles and zeros
State-space methods
Transfer functions
Vectors
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DOI10.1109/CDC.1988.194444

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Summary: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).< >
DOI:10.1109/CDC.1988.194444