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Continuous time-varying linear systems

✍ Scribed by Stefan Fröhler; Ulrich Oberst

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
170 KB
Volume
35
Category
Article
ISSN
0167-6911

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✦ Synopsis

We discuss implicit systems of ordinary linear di erential equations with (time-) variable coe cients, their solutions in the signal space of hyperfunctions according to Sato and their solution spaces, called time-varying linear systems or behaviours, from the system theoretic point of view. The basic result, inspired by an analogous one for multidimensional constant linear systems, is a duality theorem which establishes a categorical one-one correspondence between time-varying linear systems or behaviours and ÿnitely generated modules over a suitable skew-polynomial ring of di erential operators. This theorem is false for the signal spaces of inÿnitely often di erentiable functions or of meromorphic (hyper-)functions or of distributions on R. It is used to obtain various results on key notions of linear system theory. Several new algorithms for modules over rings of di erential operators and, in particular, new Gr obner basis algorithms due to Insa and Pauer make the system theoretic results e ective.

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