Tight comparison function bounds for nonlinear systems with a nonlinear L2-gain property

Nonlinear L₂-gain is a finite gain concept that generalizes the notion of conventional linear L₂-gain via the use of nonlinear comparison functions. The computation of tight comparison function bounds for this nonlinear L₂-gain property is considered. An approximation framework for these bounds is developed through the formulation of a number of equivalent optimal control problems. A Hamilton-Jacobi-Bellman partial differential equation for the value function of one of these equivalent problems is presented, facilitating the computation of approximations to the proposed bounds. An example is presented that illustrates the proposed approach.