On control by interconnection of port Hamiltonian systems

Eloisa Garcia-Canseco, R.P. Ramkrishna Pasumarthy, Arjan van der Schaft, Romeo Ortega

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    Abstract: In the standard approach of control by interconnection the plant and the controller are assumed to be passive and coupled via a power–preserving interconnection— generating an overall passive system with storage function the sum of the plant and controller storage functions. To achieve stabilization of a desired equilibrium one must make this point a minimum of the new storage function. Towards this end, dynamic invariants—called Casimirs—are first computed. Restricting the dynamics to the level sets of the Casimirs, the overall storage function becomes a bona fide function of the plant states and the storage function can be shaped. Unfortunately, this procedure is applicable only if one fixes the initial conditions of the controller to some specific values. To remove this drawback we propose in this paper to carry out the stability analysis in the full plant and controller state spaces. The new storage function is then the sum of the plant and the controller Hamiltonians and an arbitrary functions of the corresponding Casimir functions. We also provide some examples which illustrate the possibilities and limitations of the new method.
    Original languageUndefined
    Title of host publicationProceedings of the 16th IFAC World Congress
    EditorsP. Piztek
    Place of PublicationPrague
    PublisherInternational Federation of Automatic Control
    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

    Publication series



    Conference16th IFAC World Congress 2005
    CountryCzech Republic
    Internet address


    • IR-69199
    • EWI-16857
    • Interconnection
    • METIS-228698
    • Lyapunov stability

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