On the relationships between induced ℓ∞-gain and various notions of dissipativity

Several approaches to the dissipativity characterization of ℓ^∞-gain performance measures are compared and contrasted. Points of comparison include whether the given characterization is both necessary and sufficient or merely sufficient for ℓ^∞-gain, whether there is a simple relationship between the gain parameter (or gain function) and the supply rate or performance output, and whether the characterization employs auxiliary nonlinear filters. There is also a discussion of the roles of different types of bias in classical ℓ^P-gain performance criteria.