Characterization of well-posedness of piecewise linear systems

J.I. Imura, Arjan van der Schaft

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    Abstract

    One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\'eodory. The concepts of jump solutions or a sliding mode are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multi-modal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-posed.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 1998

    Publication series

    NameMemorandum / Department of Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1475
    ISSN (Print)0169-2690

    Keywords

    • MSC-90C33
    • MSC-93A30
    • EWI-3295
    • IR-65664
    • MSC-93B99

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