# Boundary Control Systems and the System Node

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

4 Citations (Scopus)

### Abstract

In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operator $\mathcal{S}:= \left[ \begin{smallmatrix} A\& B\, \\ C\& D \end{smallmatrix}\right]:D(S) \rightarrow \vects{ X }{ Y }$ where $X$ is the state space and $Y$ is the output space. Here we give results which show how to find the top part of this operator and its domain in an easy way. For a class of boundary control systems, associated with a skew-symmetric differential operator, we completely identify the system node. Some results about stability and approximate observability are presented for this class of systems.
Original language Undefined Proceedings of the 16th IFAC World Congress P Horacek, M Simandl, P Zitek Amsterdam International Federation of Automatic Control - 6 978-0-08-045108-4 Published - Jul 2005 16th IFAC World Congress 2005 - Prague, Czech RepublicDuration: 3 Jul 2005 → 8 Jul 2005Conference number: 16http://www.utia.cas.cz/news/608

### Publication series

Name Elsevier

### Conference

Conference 16th IFAC World Congress 2005 Czech Republic Prague 3/07/05 → 8/07/05 http://www.utia.cas.cz/news/608

### Keywords

• EWI-8283
• IR-63719
• METIS-225037

### Cite this

Villegas, J. A., Le Gorrec, Y., Zwart, H. J., & van der Schaft, A. (2005). Boundary Control Systems and the System Node. In P. Horacek, M. Simandl, & P. Zitek (Eds.), Proceedings of the 16th IFAC World Congress (pp. -). Amsterdam: International Federation of Automatic Control.
Villegas, J.A. ; Le Gorrec, Y. ; Zwart, Heiko J. ; van der Schaft, Arjan. / Boundary Control Systems and the System Node. Proceedings of the 16th IFAC World Congress. editor / P Horacek ; M Simandl ; P Zitek. Amsterdam : International Federation of Automatic Control, 2005. pp. -
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title = "Boundary Control Systems and the System Node",
abstract = "In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operator $\mathcal{S}:= \left[ \begin{smallmatrix} A\& B\, \\ C\& D \end{smallmatrix}\right]:D(S) \rightarrow \vects{ X }{ Y }$ where $X$ is the state space and $Y$ is the output space. Here we give results which show how to find the top part of this operator and its domain in an easy way. For a class of boundary control systems, associated with a skew-symmetric differential operator, we completely identify the system node. Some results about stability and approximate observability are presented for this class of systems.",
keywords = "EWI-8283, IR-63719, METIS-225037",
author = "J.A. Villegas and {Le Gorrec}, Y. and Zwart, {Heiko J.} and {van der Schaft}, Arjan",
year = "2005",
month = "7",
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isbn = "978-0-08-045108-4",
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Villegas, JA, Le Gorrec, Y, Zwart, HJ & van der Schaft, A 2005, Boundary Control Systems and the System Node. in P Horacek, M Simandl & P Zitek (eds), Proceedings of the 16th IFAC World Congress. International Federation of Automatic Control, Amsterdam, pp. -, 16th IFAC World Congress 2005, Prague, Czech Republic, 3/07/05.

Boundary Control Systems and the System Node. / Villegas, J.A.; Le Gorrec, Y.; Zwart, Heiko J.; van der Schaft, Arjan.

Proceedings of the 16th IFAC World Congress. ed. / P Horacek; M Simandl; P Zitek. Amsterdam : International Federation of Automatic Control, 2005. p. -.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Boundary Control Systems and the System Node

AU - Villegas, J.A.

AU - Le Gorrec, Y.

AU - Zwart, Heiko J.

AU - van der Schaft, Arjan

PY - 2005/7

Y1 - 2005/7

N2 - In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operator $\mathcal{S}:= \left[ \begin{smallmatrix} A\& B\, \\ C\& D \end{smallmatrix}\right]:D(S) \rightarrow \vects{ X }{ Y }$ where $X$ is the state space and $Y$ is the output space. Here we give results which show how to find the top part of this operator and its domain in an easy way. For a class of boundary control systems, associated with a skew-symmetric differential operator, we completely identify the system node. Some results about stability and approximate observability are presented for this class of systems.

AB - In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operator $\mathcal{S}:= \left[ \begin{smallmatrix} A\& B\, \\ C\& D \end{smallmatrix}\right]:D(S) \rightarrow \vects{ X }{ Y }$ where $X$ is the state space and $Y$ is the output space. Here we give results which show how to find the top part of this operator and its domain in an easy way. For a class of boundary control systems, associated with a skew-symmetric differential operator, we completely identify the system node. Some results about stability and approximate observability are presented for this class of systems.

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KW - IR-63719

KW - METIS-225037

M3 - Conference contribution

SN - 978-0-08-045108-4

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BT - Proceedings of the 16th IFAC World Congress

A2 - Horacek, P

A2 - Simandl, M

A2 - Zitek, P

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Villegas JA, Le Gorrec Y, Zwart HJ, van der Schaft A. Boundary Control Systems and the System Node. In Horacek P, Simandl M, Zitek P, editors, Proceedings of the 16th IFAC World Congress. Amsterdam: International Federation of Automatic Control. 2005. p. -