Nonlinear ℒ2-gain analysis via a cascade

A nonlinear ℒ
₂
-gain property that generalizes the conventional (linear) notion of ℒ
₂
-gain for finite dimensional dynamical systems is studied. In particular, an optimization-based approximation strategy that facilitates computation of gain bounds via a cascade is presented. The cascade in question consists of the dynamical system under test, driven by a nonlinear “energy saturation” operator that limits the energy delivered to that system. The main advantage of this approach is demonstrated to be improved regularity properties of the value function. This is demonstrated via a specific energy saturation operator and a simple example.