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Frequency-Domain Bounds for the Multiconductor Telegrapher’s Equation
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0003-3329-436X
Imperial College London, Department of Electrical and Electronic Engineering, London, U.K.
Eindhoven University of Technology, Department of Electrical Engineering, Eindhoven, The Netherlands.
Imperial College London, Department of Electrical and Electronic Engineering, London, U.K., SW7 2AZ; Aalborg University, Department of Electronic Systems, Aalborg Øst, Denmark, 9220; University of Trieste, Department of Engineering and Architecture, Trieste, Italy.
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2026 (English)In: IEEE Transactions on Circuits and Systems Part 1: Regular Papers, ISSN 1549-8328, E-ISSN 1558-0806, Vol. 73, no 7, p. 4675-4685Article in journal (Refereed) Published
Abstract [en]

We establish mathematical bounds on the chain, ABCD and immittance matrices of a multiconductor transmission line, based on the Telegrapher’s equation. Closed-form expressions for those matrices are also presented. Existing results that hold on the imaginary axis are extended to the complex plane, without reliance on a diagonalizability assumption that is prevalent in the literature. Therefore, the results remain valid under arbitrary arrangements of the conducting wires, which include electrical faults. The analysis ultimately reveals important system-theoretic implications of the Telegrapher’s equation, which are of general relevance to control, power systems, and signal processing involving multiconductor transmission lines.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2026. Vol. 73, no 7, p. 4675-4685
Keywords [en]
Circuit theory, control theory, distributed parameter systems, infinite-dimensional systems, linear systems, network theory, transmission lines
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-378555DOI: 10.1109/TCSI.2026.3661865ISI: 001708249700001Scopus ID: 2-s2.0-105031853951OAI: oai:DiVA.org:kth-378555DiVA, id: diva2:2047876
Note

QC 20260703

Available from: 2026-03-23 Created: 2026-03-23 Last updated: 2026-07-03Bibliographically approved

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Selvaratnam, DanielSandberg, Henrik

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Decision and Control Systems (Automatic Control)
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