Equivalence between classes of multipliers for slope-restricted nonlinearities

    Research output: Contribution to journalArticlepeer-review

    174 Downloads (Pure)

    Abstract

    Different classes of multipliers have been proposed in the literature for obtaining stability criteria using passivity theory, integral quadratic constraint (IQC) theory or Lyapunov theory. Some of these classes of multipliers can be applied with slope-restricted nonlinearities. In this paper the concept of phase-containment is defined and it is shown that several classes are phase-contained within the class of Zames-Falb multipliers. There are two main consequences: firstly it follows that the class of Zames-Falb multipliers remains, to date, the widest class of available multipliers for slope-restricted nonlinearities; secondly further restrictions may be avoided when exploiting the parametrization of the other classes of multipliers. © 2013 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)1732-1740
    Number of pages8
    JournalAutomatica
    Volume49
    Issue number6
    DOIs
    Publication statusPublished - Jun 2013

    Keywords

    • Absolute stability
    • Slope-restricted nonlinearities
    • Zames-Falb multipliers

    Fingerprint

    Dive into the research topics of 'Equivalence between classes of multipliers for slope-restricted nonlinearities'. Together they form a unique fingerprint.

    Cite this