  Equilibrium-independent dissipativity (EID) is a recently introduced system
property which requires a system to be dissipative with respect to any forced
equilibrium configuration. This paper is a detailed examination of EID with
quadratic supply rates for a common class of nonlinear control-affine systems.
We provide an algebraic characterization of EID for such systems in the spirit
of the Hill-Moylan lemma, where the usual stability condition is replaced by an
incremental stability condition. Based on this characterization, we state
results concerning internal stability, feedback stability, and absolute
stability of EID systems. Finally, we study EID for discrete-time systems,
providing the relevant definitions and an analogous Hill-Moylan-type
characterization. Results for both continuous-time and discrete-time systems
are illustrated through examples on physical systems and convex optimization
algorithms.
