A weak L2-gain property for nonlinear systems

Nonlinear L2-gain is a generalization of the conventional (linear) notion of L2-gain in which the linear scaling of input energy is replaced by a nonlinear comparison function scaling. In this paper, this nonlinear L2-gain property is formalized as being strictly weaker than the conventional linear property. This is achieved by appealing to existing results in the literature that demonstrate qualitative equivalences between linear L2-gain and input-to-state stability (ISS), and between nonlinear L2-gain and the strictly weaker integral ISS (iISS) property.

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