Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation

Bernard M.J. Maschke, Romeo Ortega, Arjan J. van der Schaft

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

    Abstract

    We propose a constructive procedure to modify the total energy function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for non-zero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a series of Casimir functions (i.e., first integrals) can be easily constructed. For linear systems the resulting Lyapunov function is the incremental energy, thus our derivations provide a physical explanation to it. An easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given. Some examples that illustrate the method are given.
    Original languageEnglish
    Title of host publicationProceedings 37th IEEE Conference on Decision and Control, CDC 1998
    Place of PublicationLos Alamitos, CA
    PublisherIEEE
    Pages3599-3604
    Number of pages6
    ISBN (Print)0-7803-4394-8
    DOIs
    Publication statusPublished - 16 Dec 1998
    Event37th IEEE Conference on Decision and Control, CDC 1998 - Hyatt Regency Westshore, Tampa, United States
    Duration: 16 Dec 199818 Dec 1998
    Conference number: 37

    Publication series

    NameIEEE Conference on Decision and Control, CDC
    PublisherIEEE
    Volume1998
    ISSN (Print)0191-2216

    Conference

    Conference37th IEEE Conference on Decision and Control, CDC 1998
    Abbreviated titleCDC
    Country/TerritoryUnited States
    CityTampa
    Period16/12/9818/12/98

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