Stability and Stabilization of a Class of Boundary Control Systems

J.A. Villegas; Heiko J. Zwart; Y. Le Gorrec; B.M. Maschke; Arjan van der Schaft

doi:10.1109/CDC.2005.1582762

Stability and Stabilization of a Class of Boundary Control Systems

J.A. Villegas
, Heiko J. Zwart
, Y. Le Gorrec
, B.M. Maschke
, Arjan van der Schaft

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

31 Citations (Scopus)

302 Downloads (Pure)

Abstract

We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance energy-preserving system, as well as scattering energy-preserving system. For the first type of systems we consider (static and dynamic) feedback stabilization by means of boundary control. For the scattering energy-preserving systems we give conditions for which the system is either asymptotically or exponentially stable.

Original language	Undefined
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference ECC
Place of Publication	USA
Publisher	IEEE
Pages	3850-3855
Number of pages	6
ISBN (Print)	0-7803-9568-9
DOIs	https://doi.org/10.1109/CDC.2005.1582762
Publication status	Published - Dec 2005
Event	44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005 - Melia Seville, Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005 Conference number: 44

Publication series

Name
Publisher	IEEE
Volume	078039

Conference

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

Keywords

EWI-8282
METIS-225811
IR-53272

Access to Document

10.1109/CDC.2005.1582762

Cite this

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title = "Stability and Stabilization of a Class of Boundary Control Systems",

abstract = "We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance energy-preserving system, as well as scattering energy-preserving system. For the first type of systems we consider (static and dynamic) feedback stabilization by means of boundary control. For the scattering energy-preserving systems we give conditions for which the system is either asymptotically or exponentially stable.",

keywords = "EWI-8282, METIS-225811, IR-53272",

author = "J.A. Villegas and Zwart, \{Heiko J.\} and \{Le Gorrec\}, Y. and B.M. Maschke and \{van der Schaft\}, Arjan",

year = "2005",

month = dec,

doi = "10.1109/CDC.2005.1582762",

language = "Undefined",

isbn = "0-7803-9568-9",

publisher = "IEEE",

pages = "3850--3855",

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

address = "United States",

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

}

Villegas, JA, Zwart, HJ, Le Gorrec, Y, Maschke, BM & van der Schaft, A 2005, Stability and Stabilization of a Class of Boundary Control Systems. in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference ECC. IEEE, USA, pp. 3850-3855, 44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1582762

Stability and Stabilization of a Class of Boundary Control Systems. / Villegas, J.A.; Zwart, Heiko J.; Le Gorrec, Y. et al.
Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference ECC. USA: IEEE, 2005. p. 3850-3855.

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

TY - GEN

T1 - Stability and Stabilization of a Class of Boundary Control Systems

AU - Villegas, J.A.

AU - Zwart, Heiko J.

AU - Le Gorrec, Y.

AU - Maschke, B.M.

AU - van der Schaft, Arjan

N1 - Conference code: 44

PY - 2005/12

Y1 - 2005/12

N2 - We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance energy-preserving system, as well as scattering energy-preserving system. For the first type of systems we consider (static and dynamic) feedback stabilization by means of boundary control. For the scattering energy-preserving systems we give conditions for which the system is either asymptotically or exponentially stable.

AB - We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance energy-preserving system, as well as scattering energy-preserving system. For the first type of systems we consider (static and dynamic) feedback stabilization by means of boundary control. For the scattering energy-preserving systems we give conditions for which the system is either asymptotically or exponentially stable.

KW - EWI-8282

KW - METIS-225811

KW - IR-53272

U2 - 10.1109/CDC.2005.1582762

DO - 10.1109/CDC.2005.1582762

M3 - Conference contribution

SN - 0-7803-9568-9

SP - 3850

EP - 3855

BT - Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference ECC

PB - IEEE

CY - USA

T2 - 44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005

Y2 - 12 December 2005 through 15 December 2005

ER -