Universität zu Köln

Riaza, Ricardo ORCID: 0000-0003-0868-4446 and Tischendorf, Caren ORCID: 0000-0002-8421-7199 (2010). The hyperbolicity problem in electrical circuit theory. Math. Meth. Appl. Sci., 33 (17). S. 2037 - 2050. MALDEN: WILEY-BLACKWELL. ISSN 0170-4214

Full text not available from this repository.

Abstract

The time-domain characterization of qualitative properties of electrical circuits requires the combined use of mathematical concepts and tools coming from digraph theory, applied linear algebra and the theory of differential-algebraic equations. This applies, in particular, to the analysis of the circuit hyperbolicity, a key qualitative feature regarding oscillations. A linear circuit is hyperbolic if all of its eigenvalues are away from the imaginary axis. Characterizing the hyperbolicity of a strictly passive circuit family is a two-fold problem, which involves the description of (so-called topologically non-hyperbolic) configurations yielding purely imaginary eigenvalues (PIEs) for all circuit parameters and, when this is not the case, the description of the parameter values leading to PIEs. A full characterization of the problem is shown here to be feasible for certain circuit topologies. The analysis is performed in terms of differential-algebraic branch-oriented circuit models, which drive the spectral study to a matrix pencil setting, and makes systematic use of a matrix-based formulation of digraph properties. Several examples illustrate the results. Copyright (C) 2010 John Wiley & Sons, Ltd.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Riaza, Ricardo UNSPECIFIED orcid.org/0000-0003-0868-4446 UNSPECIFIED Tischendorf, Caren UNSPECIFIED orcid.org/0000-0002-8421-7199 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-492188
DOI:	10.1002/mma.1312
Journal or Publication Title:	Math. Meth. Appl. Sci.
Volume:	33
Number:	17
Page Range:	S. 2037 - 2050
Date:	2010
Publisher:	WILEY-BLACKWELL
Place of Publication:	MALDEN
ISSN:	0170-4214
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CAPACITOR-ONLY CUTSETS; NON-LINEAR NETWORKS; GEOMETRIC-PROPERTIES; NONLINEAR NETWORKS; LOOPS; OSCILLATIONS; SYSTEMS; MATRIX Multiple languages Mathematics, Applied Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/49218