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

Dissipativity and feedback passivity properties in nonlinear multiple-inputmultiple-output (MIMO) discrete-time systems are examined. Three main results are presented. First, necessary and sufficient conditions for the characterization of a class ofdissipative nonlinear MIMO discrete-time systems in general form are proposed. The classof dissipativity treated is referred to as Quadratic Storage Supply-dissipativity. The conditionsexisting in the literature, addressed as Kalman-Yakubovich-Popov conditions, for thedissipative, passive or lossless cases, are derived from the proposed dissipativity characterization. Second, some relative degree-related properties of nonlinear MIMO QuadraticStorage-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 propertiesof the relative degree and zero dynamics is analyzed. Quadratic Storage-passive systemsare considered. The feedback passivity methodology is illustrated by means of a class ofsystems modelling different discrete dynamics with physical interpretation.

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