Exponential stability of a class of boundary control systems

J.A. Villegas, Heiko J. Zwart, Yann Le Gorrec, B.M. Maschke

    Research output: Contribution to journalArticleAcademicpeer-review

    84 Citations (Scopus)
    313 Downloads (Pure)


    We study a class of partial differential equations (with variable coefficients) on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we provide simple tools to check exponential stability. This class is general enough to include models of flexible structures, traveling waves, heat exchangers, and bioreactors among others. The result is based on the use of a generating function (the energy for physical systems) and an inequality condition at the boundary. Furthermore, based on the port Hamiltonian approach, we give a constructive method to reduce this inequality to a simple matrix inequality.
    Original languageUndefined
    Article number10.1109/TAC.2008.2007176
    Pages (from-to)142-147
    Number of pages6
    JournalIEEE transactions on automatic control
    Issue number1
    Publication statusPublished - Jan 2009


    • Stability
    • EWI-15878
    • IR-67844
    • METIS-263971
    • MSC-93C20

    Cite this