Topological analysis of qualitative features in electrical circuit theory
Please always quote using this URN:urn:nbn:de:0296-matheon-1666
- Several qualitative properties of equilibria in electrical circuits are analyzed in this paper. Specifically, non-singularity, hyperbolicity, and asymptotic stability are addressed in terms of the circuit topology, which is captured through the use of Modified Nodal Analysis (MNA) models. The differential-algebraic or semistate nature of these models drives the analysis of the spectrum to a matrix pencil setting, and puts the results beyond the ones already known for state-space models, unfeasible in many actual problems. The topological conditions arising in this qualitative study are proved independent of those supporting the index, and therefore they apply to both index-1 and index-2 configurations. The analysis combines results coming from graph theory, matrix analysis, matrix pencil theory, and Lyapunov theory for DAEs. The study is restricted to problems with independent sources; qualitative properties of circuits including controlled sources are the focus of future research.
Author: | Ricardo Riaza, Caren Tischendorf |
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URN: | urn:nbn:de:0296-matheon-1666 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/09/30 |
Release Date: | 2004/09/30 |
Preprint Number: | 159 |