QSS-dissipativity and feedback QS-passivity of nonlinear discrete-time systems

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    Dissipativity and feedback passivity properties in nonlinear multiple-input multiple-output (MIMO) discrete-time systems are examined. Three main results are presented. First, necessary and sufficient conditions for the characterization of a class of dissipative nonlinear MIMO discrete-time systems in general form are proposed. The class of dissipativity treated is referred to as Quadratic Storage Supply-dissipativity. The conditions existing in the literature, addressed as Kalman-Yakubovich-Popov conditions, for the dissipative, passive or lossless cases, are derived from the proposed dissipativity characterization. Second, some relative degree-related properties of nonlinear MIMO Quadratic Storage-passive systems which are affine in the input are stated. Third, the problem of rendering a nonlinear affine-in-input MIMO discrete-time system passive using the properties of the relative degree and zero dynamics is analyzed. Quadratic Storage-passive systems are considered. The feedback passivity methodology is illustrated by means of a class of systems modelling different discrete dynamics with physical interpretation. Copyright © 2007 Watam Press.
    Original languageEnglish
    Pages (from-to)47-63
    Number of pages16
    JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
    Issue number1
    Publication statusPublished - Feb 2007


    • Discrete-time systems
    • Dissipativity
    • Feedback passivity
    • Feedback stabilization
    • Nonlinear systems


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