Complementarity modeling of hybrid systems

A.J. van der Schaft, J.M. Schumacher

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    A complementarity framework is described for the modeling of certain classes of mixed continuous/discrete dynamical systems. The use of such a framework is well-known for mechanical systems with inequality constraints, but we give a more general formulation which applies for instance also to systems with relays in a feedback loop. The main theoretical results in the paper are concerned with uniqueness of smooth continuations; the solution of this problem requires the construction of a map from the continuous state to the discrete state. A crucial technical tool is the so-called linear complementarity problem (LCP); we introduce various generalizations of this problem. Specific results are obtained for Hamiltonian systems, passive systems, and linear systems.
    Original languageEnglish
    Place of PublicationAmsterdam
    PublisherCentrum voor Wiskunde en Informatica
    Number of pages23
    Publication statusPublished - 1996

    Publication series

    NameReport / Department of Operations Research, Statistics, and System Theory
    ISSN (Print)0924-0659


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