Passivity and Dissipativity of a Nonlinear System and its Linearization Technical Report of the ISIS Group at the University of Notre Dame ISIS-12-008 September 2012

In this paper, we investigate when passivity for a nonlinear system can be inferred from its linearization. The nonlinear system considered here are affine in control and with feedthrough terms, in both continuous-time domain and discrete-time domain. Our main results demonstrate when the linearized system is simultaneously strict passive and strict input passive (SSIP), the nonlinear system will be SSIP as well within a neighborhood of the equilibrium point. We establish algebraic conditions under which a linear system is SSIP based on the positive real lemma. The results are extended to dissipative systems and in particular, passivity indices can be derived for a nonlinear system from the linearized system within a neighborhood of the equilibrium.

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