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A general realization theory for higher-order linear differential equations


Ravi, M; Rosenthal, J (1995). A general realization theory for higher-order linear differential equations. Systems & Control Letters, 25(5):351-360.

Abstract

In this note we show that the geometric quotient, under a natural group action, of the generalized state space systems recently considered by Schumacher, Kuijper and Geerts is algebraically isomorphic to the space of a homogeneous autoregressive system. This result essentially follows from work of Stromme published earlier in the algebraic geometry literature. In particular, these generalized state space systems represent a realization of the space of homogeneous autoregressive systems.

Abstract

In this note we show that the geometric quotient, under a natural group action, of the generalized state space systems recently considered by Schumacher, Kuijper and Geerts is algebraically isomorphic to the space of a homogeneous autoregressive system. This result essentially follows from work of Stromme published earlier in the algebraic geometry literature. In particular, these generalized state space systems represent a realization of the space of homogeneous autoregressive systems.

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16 citations in Web of Science®
13 citations in Scopus®
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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:Linear systems; Realization theory; AR-systems; Behaviors; Quot scheme; Fine moduli space; Geometric invariant theory
Language:English
Date:1995
Deposited On:19 Mar 2010 07:51
Last Modified:05 Apr 2016 13:27
Publisher:Elsevier
ISSN:0167-6911
Publisher DOI:https://doi.org/10.1016/0167-6911(94)00085-A

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