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IMA Journal of Mathematical Control and Information Advance Access originally published online on July 27, 2005
IMA Journal of Mathematical Control and Information 2006 23(1):113-126; doi:10.1093/imamci/dni047
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Institute of Mathematics and its Applications 2005; all rights reserved for permissions please email: journals.permissions@oupjournals.org

An algebraic analysis approach to linear time-varying systems

Eva Zerz**

Department of Mathematics, University of Kaiserslautern, 67663 Kaiserslautern, Germany

** Email: zerz{at}mathematik.uni-kl.de

This paper introduces an algebraic analysis approach to linear time-varying systems. The analysis is carried out in an ‘almost everywhere’ setting, i.e. the considered signals are smooth except for a set of measure zero, and the coefficients of the linear ordinary differential equations are supposed to be rational or meromorphic functions. The methodology is based on a normal form for matrices over the resulting ring of differential operators, which is a non-commutative analogue of the Smith form. This is used to establish a duality between linear time-varying systems on the one hand and modules over the ring of differential operators on the other. This correspondence is based on the fact that the signal space is an injective cogenerator when considered as a module over this ring of differential operators.

Keywords: linear ordinary differential equations with rational or meromorphic coefficients; time-varying linear systems; behavioural approach; algebraic analysis; module theory.

Received on 17 June 2004. accepted on 11 January 2005.


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