On the inverse scattering of star-shape LC-networks

Filippo Visco Comandini; Mazyar Mirrahimi; Michel Sorine

doi:10.1109/CDC.2008.4738787

On the inverse scattering of star-shape LC-networks

Filippo Visco Comandini
, Mazyar Mirrahimi
, Michel Sorine

INRIA Rocquencourt

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schrödinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the existence of a unique self-adjoint extension of the mentioned Schrödinger operator. While the graph consists of a number of infinite branches and a number finite ones, all joining at a central node, we provide a construction of the scattering solutions. Under non-degenerate circumstances (different wave travelling times for finite branches), we show that the study of the reflection coefficient in the high-frequency regime must provide us with the number of the infinite branches as well as the the wave travelling times for finite ones.

Original language	English
Title of host publication	Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2075-2080
Number of pages	6
ISBN (Print)	9781424431243
DOIs	https://doi.org/10.1109/CDC.2008.4738787
Publication status	Published - 1 Jan 2008
Externally published	Yes
Event	47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: 9 Dec 2008 → 11 Dec 2008

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	47th IEEE Conference on Decision and Control, CDC 2008
Country/Territory	Mexico
City	Cancun
Period	9/12/08 → 11/12/08

Access to Document

10.1109/CDC.2008.4738787

Cite this

Comandini, F. V., Mirrahimi, M., & Sorine, M. (2008). On the inverse scattering of star-shape LC-networks. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 2075-2080). Article 4738787 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2008.4738787

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title = "On the inverse scattering of star-shape LC-networks",

abstract = "The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schr{\"o}dinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the existence of a unique self-adjoint extension of the mentioned Schr{\"o}dinger operator. While the graph consists of a number of infinite branches and a number finite ones, all joining at a central node, we provide a construction of the scattering solutions. Under non-degenerate circumstances (different wave travelling times for finite branches), we show that the study of the reflection coefficient in the high-frequency regime must provide us with the number of the infinite branches as well as the the wave travelling times for finite ones.",

author = "Comandini, \{Filippo Visco\} and Mazyar Mirrahimi and Michel Sorine",

year = "2008",

month = jan,

day = "1",

doi = "10.1109/CDC.2008.4738787",

language = "English",

isbn = "9781424431243",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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note = "47th IEEE Conference on Decision and Control, CDC 2008 ; Conference date: 09-12-2008 Through 11-12-2008",

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Comandini, FV, Mirrahimi, M & Sorine, M 2008, On the inverse scattering of star-shape LC-networks. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4738787, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2075-2080, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 9/12/08. https://doi.org/10.1109/CDC.2008.4738787

On the inverse scattering of star-shape LC-networks. / Comandini, Filippo Visco; Mirrahimi, Mazyar; Sorine, Michel.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc., 2008. p. 2075-2080 4738787 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - On the inverse scattering of star-shape LC-networks

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AU - Mirrahimi, Mazyar

AU - Sorine, Michel

PY - 2008/1/1

Y1 - 2008/1/1

N2 - The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schrödinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the existence of a unique self-adjoint extension of the mentioned Schrödinger operator. While the graph consists of a number of infinite branches and a number finite ones, all joining at a central node, we provide a construction of the scattering solutions. Under non-degenerate circumstances (different wave travelling times for finite branches), we show that the study of the reflection coefficient in the high-frequency regime must provide us with the number of the infinite branches as well as the the wave travelling times for finite ones.

AB - The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schrödinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the existence of a unique self-adjoint extension of the mentioned Schrödinger operator. While the graph consists of a number of infinite branches and a number finite ones, all joining at a central node, we provide a construction of the scattering solutions. Under non-degenerate circumstances (different wave travelling times for finite branches), we show that the study of the reflection coefficient in the high-frequency regime must provide us with the number of the infinite branches as well as the the wave travelling times for finite ones.

UR - https://www.scopus.com/pages/publications/62949102401

U2 - 10.1109/CDC.2008.4738787

DO - 10.1109/CDC.2008.4738787

M3 - Conference contribution

AN - SCOPUS:62949102401

SN - 9781424431243

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2075

EP - 2080

BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 47th IEEE Conference on Decision and Control, CDC 2008

Y2 - 9 December 2008 through 11 December 2008

ER -

On the inverse scattering of star-shape LC-networks

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