Abstract
This article studies the telegrapher's equations with boundary port variables. Firstly, a link is made between the telegrapher's equations and a skew-symmetric linear operator on a spatial domain. Associated to this linear operator is a Dirac structure which includes the port variables on the boundary of this spatial domain. Secondly, we present all partitions of the port variables into inputs and outputs for which the state dynamics is dissipative. Particularly, we recognize the possible input-outputs for which the system is impedance energy-preserving, i.e., $\frac{1}{2}\frac{d}{dt}\|x(t)\|^2 = u(t)^T y(t)$, as well as scattering energy-preserving, i.e.,$\frac{1}{2}\frac{d}{dt}\|x(t)\|^2 = \|u(t)\|^2 -\|y(t)\|^2$. Additionally, we show how to represent the corresponding system as an abstract infinite-dimensional system, i.e., $\dot{x}(t) =Ax(t) +Bu(t)$ and $y(t) = Cx(t)+Du(t)$.
Original language | Undefined |
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Title of host publication | 16th IFAC World Congress |
Editors | P Horacek, M Simandl, P Zitek |
Place of Publication | Amsterdam |
Publisher | International Federation of Automatic Control |
Pages | - |
Number of pages | 6 |
ISBN (Print) | 978-0-08-045108-4 |
Publication status | Published - Jul 2005 |
Event | 16th IFAC World Congress 2005 - Prague, Czech Republic Duration: 3 Jul 2005 → 8 Jul 2005 Conference number: 16 http://www.utia.cas.cz/news/608 |
Publication series
Name | |
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Publisher | Elsevier |
Conference
Conference | 16th IFAC World Congress 2005 |
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Country/Territory | Czech Republic |
City | Prague |
Period | 3/07/05 → 8/07/05 |
Internet address |
Keywords
- IR-63720
- EWI-8285
- METIS-225036