# Port Representations of the Telegrapher's Equations

J.A. Villegas, Heiko J. Zwart, Arjan van der Schaft

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

## 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 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

• IR-63720
• EWI-8285
• METIS-225036