Two dual classes of time-varying well-posed linear systems constructed from passive systems

George Weiss; Roland Schnaubelt

doi:10.1109/CDC.2005.1583102

Two dual classes of time-varying well-posed linear systems constructed from passive systems

George Weiss^*
, Roland Schnaubelt

^*Corresponding author for this work

Imperial College London
Fachbereich Mathem. und Informatik
Martin Luther University Halle-Wittenberg

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

Abstract

We introduce two classes of well-posed linear time-varying (LTV) systems. Each of these can be constructed easily, starting from a time-invariant scattering-passive system, by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of LTV systems are motivated by physical examples, such as an electromagnetic field around a moving object. To prove the well-posedness of these LTV systems, we use the Lax-Phillips semigroup induced by a well-posed linear system, as in scattering theory. We modify this semigroup to obtain a Lax-Phillips type evolution family.

Original language	English
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Publisher	IEEE Computer Society
Pages	5883-5886
Number of pages	4
ISBN (Print)	0780395689, 9780780395688
DOIs	https://doi.org/10.1109/CDC.2005.1583102
State	Published - 2005
Externally published	Yes
Event	Joint 44th IEEE Conference on Decision and Control and the 8th European Control Conference, CDC-ECC 2005 - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Conference

Conference	Joint 44th IEEE Conference on Decision and Control and the 8th European Control Conference, CDC-ECC 2005
Country/Territory	Spain
City	Seville
Period	12/12/05 → 15/12/05

Access to Document

10.1109/CDC.2005.1583102

Cite this

Weiss, G., & Schnaubelt, R. (2005). Two dual classes of time-varying well-posed linear systems constructed from passive systems. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 5883-5886). Article 1583102 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). IEEE Computer Society. https://doi.org/10.1109/CDC.2005.1583102

Weiss, George ; Schnaubelt, Roland. / Two dual classes of time-varying well-posed linear systems constructed from passive systems. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. IEEE Computer Society, 2005. pp. 5883-5886 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05).

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title = "Two dual classes of time-varying well-posed linear systems constructed from passive systems",

abstract = "We introduce two classes of well-posed linear time-varying (LTV) systems. Each of these can be constructed easily, starting from a time-invariant scattering-passive system, by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of LTV systems are motivated by physical examples, such as an electromagnetic field around a moving object. To prove the well-posedness of these LTV systems, we use the Lax-Phillips semigroup induced by a well-posed linear system, as in scattering theory. We modify this semigroup to obtain a Lax-Phillips type evolution family.",

author = "George Weiss and Roland Schnaubelt",

year = "2005",

doi = "10.1109/CDC.2005.1583102",

language = "אנגלית",

isbn = "0780395689",

series = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

publisher = "IEEE Computer Society",

pages = "5883--5886",

booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

address = "ארצות הברית",

note = "Joint 44th IEEE Conference on Decision and Control and the 8th European Control Conference, CDC-ECC 2005 ; Conference date: 12-12-2005 Through 15-12-2005",

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Weiss, G & Schnaubelt, R 2005, Two dual classes of time-varying well-posed linear systems constructed from passive systems. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583102, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, IEEE Computer Society, pp. 5883-5886, Joint 44th IEEE Conference on Decision and Control and the 8th European Control Conference, CDC-ECC 2005, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583102

Two dual classes of time-varying well-posed linear systems constructed from passive systems. / Weiss, George; Schnaubelt, Roland.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. IEEE Computer Society, 2005. p. 5883-5886 1583102 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

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

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Weiss G, Schnaubelt R. Two dual classes of time-varying well-posed linear systems constructed from passive systems. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. IEEE Computer Society. 2005. p. 5883-5886. 1583102. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1583102

Two dual classes of time-varying well-posed linear systems constructed from passive systems

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