Discrete-Time Negative Imaginary Systems

Augusto Ferrante, Alexander Lanzon, Lorenzo Ntogramatzidis

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    Abstract

    In this paper we introduce the notion of a discrete-time negative imaginary system and we investigate its relations with discrete-time positive
    real system theory. In the framework presented here, discrete-time negative imaginary systems are defined in terms of a sign condition
    that must be satisfied in a domain of analyticity of the transfer function, in analogy with the case of discrete-time positive real functions,
    as well as analogously to the continuous-time case. This means in particular that we do not need to restrict our notions and definitions
    to systems with rational transfer functions. We also provide a discrete-time counterpart of the different notions that have appeared so
    far in the literature within the framework of strictly positive real and in the more recent theory of strictly negative imaginary systems,
    and to show how these notions are characterized and linked to each other. Stability analysis results for the feedback interconnection of
    discrete-time negative imaginary systems are also derived.
    Original languageEnglish
    Pages (from-to)1-10
    Number of pages10
    JournalAutomatica
    Volume79
    Early online date2 Mar 2017
    DOIs
    Publication statusPublished - 2017

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