GENERALIZED BEZOUT IDENTITY

Authors
POMMARET JF QUADRAT A
Citation
Jf. Pommaret et A. Quadrat, GENERALIZED BEZOUT IDENTITY, Applicable algebra in engineering, communication and computing, 9(2), 1998, pp. 91-116
Citations number
42
Categorie Soggetti
Mathematics,"Computer Science Theory & Methods","Computer Science Interdisciplinary Applications",Mathematics,"Computer Science Theory & Methods","Computer Science Interdisciplinary Applications
Journal title
Applicable algebra in engineering, communication and computing → ACNP
ISSN journal
09381279
Volume
9
Issue
2
Year of publication
1998
Pages
91 - 116
Database
ISI
SICI code
0938-1279(1998)9:2<91:>2.0.ZU;2-Z
Abstract
We describe a new approach of the generalized Bezout identity for line ar time-varying ordinary differential control systems. We also explain when and how it can be extended to linear partial differential contro l systems. We show that it only depends on the algebraic nature of the differential module determined by the equations of the system. This f ormulation shows that the generalized Bezout identity is equivalent to the splitting of an exact differential sequence formed by the control system and its parametrization. This point of view gives a new algebr aic and geometric interpretation of the entries of the generalized Bez out identity.