Decision algorithm for the stability of planar switching linear systems

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    Abstract

    This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyper planes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not.
    Original languageUndefined
    Title of host publicationProceedings of the 18th international symposium on mathematical theory of networks & systems
    Place of PublicationUSA
    PublisherSIAM
    Pages11
    Number of pages11
    ISBN (Print)not assigned
    Publication statusPublished - Aug 2008

    Publication series

    Name
    PublisherSIAM
    Number2008/16200

    Keywords

    • EWI-14798
    • METIS-255078
    • IR-65267

    Cite this

    Daws, C. F., Langerak, R., & Polderman, J. W. (2008). Decision algorithm for the stability of planar switching linear systems. In Proceedings of the 18th international symposium on mathematical theory of networks & systems (pp. 11). USA: SIAM.