Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

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    Abstract

    The topic of this paper is the analysis of stability for a class of switched linearsystems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions.
    Original languageUndefined
    Title of host publication44th IEEE Conference on Decision and Control and European Control Conference ECC 2005
    Place of PublicationLos Alamitos
    PublisherIEEE
    Pages4867-4872
    Number of pages6
    ISBN (Print)0-7803-9567-0
    DOIs
    Publication statusPublished - 11 Dec 2005
    Event44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005 - Melia Seville, Seville, Spain
    Duration: 12 Dec 200515 Dec 2005
    Conference number: 44

    Publication series

    Name
    PublisherIEEE

    Conference

    Conference44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005
    Abbreviated titleCDC-ECC
    CountrySpain
    CitySeville
    Period12/12/0515/12/05

    Keywords

    • Automata
    • EWI-1539
    • IR-54781
    • Switched systems
    • METIS-229270
    • Stability of hybrid systems

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