Necessary and sufficient conditions for a class of dissipative nonlinear multiinput multi-output discrete-time systems are given. 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. Feedback passivity is solved for a class of multi-input multi-output nonlinear discrete-time systems affine in the control input using the properties of the relative degree and zero dynamics of the non-passive system. This is the first solution presented in the literature to such a problem in the discrete-time setting. The passification methodology is illustrated by means of an example.

This paper is devoted to the study of the feedback passivity property in nonlinear discrete-time systems. The relative degree and zero dynamics of the non-passive system are related to the feedback passivity of the system. Two main results are presented. First, some relative degreerelated properties of passive systems in general form are stated. Second, sufficient conditions in order to render a multiple-input multiple-output (MIMO) system passive by means of a static state feedback control law are obtained.

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