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On dynamic feedback compensation and compactification of systems


Rosenthal, J (1994). On dynamic feedback compensation and compactification of systems. SIAM Journal on Control and Optimization, 32(1):279-296.

Abstract

This paper introduces a compactification of the space of proper $p \times m$ transfer functions with a fixed McMillan degree $n$. Algebraically, this compactification has the structure of a projective variety and each point of this variety can be given an interpretation as a certain autoregressive system in the sense of Willems. It is shown that the pole placement map with dynamic compensators turns out to be a central projection from this compactification to the space of closed-loop polynomials. Using this geometric point of view, necessary and sufficient conditions are given when a strictly proper or proper system can be generically pole assigned by a complex dynamic compensator of McMillan degree $q$. ©1994 Society for Industrial and Applied Mathematics

Abstract

This paper introduces a compactification of the space of proper $p \times m$ transfer functions with a fixed McMillan degree $n$. Algebraically, this compactification has the structure of a projective variety and each point of this variety can be given an interpretation as a certain autoregressive system in the sense of Willems. It is shown that the pole placement map with dynamic compensators turns out to be a central projection from this compactification to the space of closed-loop polynomials. Using this geometric point of view, necessary and sufficient conditions are given when a strictly proper or proper system can be generically pole assigned by a complex dynamic compensator of McMillan degree $q$. ©1994 Society for Industrial and Applied Mathematics

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:multivariable systems, dynamic feedback compensation, compactification, central projection, autoregressive systems
Language:English
Date:1994
Deposited On:19 Mar 2010 16:20
Last Modified:06 Dec 2017 21:07
Publisher:Society for Industrial and Applied Mathematics
ISSN:0363-0129
Publisher DOI:https://doi.org/10.1137/S036301299122133X

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