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 languageUndefined
    Title of host publication16th IFAC World Congress
    EditorsP Horacek, M Simandl, P Zitek
    Place of PublicationAmsterdam
    PublisherInternational Federation of Automatic Control
    Pages-
    Number of pages6
    ISBN (Print)978-0-08-045108-4
    Publication statusPublished - Jul 2005
    Event16th IFAC World Congress 2005 - Prague, Czech Republic
    Duration: 3 Jul 20058 Jul 2005
    Conference number: 16
    http://www.utia.cas.cz/news/608

    Publication series

    Name
    PublisherElsevier

    Conference

    Conference16th IFAC World Congress 2005
    CountryCzech Republic
    CityPrague
    Period3/07/058/07/05
    Internet address

    Keywords

    • IR-63720
    • EWI-8285
    • METIS-225036

    Cite this