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Title: Some applications of an Implicit Duality Theorem to connections of structures of special types including Dirac and reciprocal structures
Issue Date: 2002
Citation: SYSTEMS & CONTROL LETTERS, 45(2), 87-95
Abstract: In this paper, we present some applications of an Implicit Duality Theorem which was originally a folklore result on Ideal Transformers in Electrical Network Theory. We show, among other things, that results on reciprocal networks (due to Tellegen (Proc. Inst. Radio Engrs. 14 (1953) 265), and Dirac Structures (due to van der Schaft (in: J.W. Polderman, H.L. Trentelman (Eds.), From Intelligent Control to Behavioural Systems. University of Groningen Press) follow as a consequence. These results have the form 'interconnection of structures of a particular kind yields a structure of the same kind'. Also discussed is the question 'given smaller structures of a given kind and a desired structure of the same kind, can the former be interconnected to yield the latter?'. We also indicate the range of possible generalizations of this result. (C) 2002 .
ISSN: 0167-6911
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