# 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

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

## Citations

30 citations in Web of Science®
27 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics multivariable systems, dynamic feedback compensation, compactification, central projection, autoregressive systems English 1994 19 Mar 2010 16:20 05 Apr 2016 13:28 Society for Industrial and Applied Mathematics 0363-0129 https://doi.org/10.1137/S036301299122133X
Permanent URL: https://doi.org/10.5167/uzh-22641