Well-posedness and Regularity of Hyperbolic Boundary Control Systems on a One-dimensional Spatial Domain

Heiko J. Zwart, Yann Le Gorrec, Bernard Maschke, Javier Villegas

    Research output: Contribution to journalArticleAcademicpeer-review

    55 Citations (Scopus)

    Abstract

    We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.
    Original languageEnglish
    Pages (from-to)1077-1093
    Number of pages17
    JournalESAIM: Control, Optimization and Calculus of Variations
    Volume16
    Issue number4
    DOIs
    Publication statusPublished - Oct 2010

    Keywords

    • 93C20
    • 35L40
    • 35F15
    • 37Kxx

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