Some remarks on duality over a commutative ring

M. Di Loreto, J.F. Lafay and J.J. Loiseau

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 76, issue 5, 375-387

Abstract: This paper addresses the duality problem for dynamical, linear, time-invariant systems defined over a ring. The duality principle is at the core of theoretical results for systems defined over a field, but this principle can not be applied for systems over a ring. From the definition of controlled and conditioned invariant submodules in the geometric approach, we analyze the relationships among various notions of invariance, using the concept of orthogonal submodule. These logical relations are summarized in two non-equivalent schemes.

Keywords: Geometric approach; Time-delay system; Ring; Submodule; Duality; Orthogonality; Closure; Controlled invariance; Conditioned invariance; State feedback; Output injection (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475407001693
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:76:y:2008:i:5:p:375-387

DOI: 10.1016/j.matcom.2007.04.004

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().