  Frequency domain analysis of linear time-invariant (LTI) systems in feedback
with static nonlinearities is a classical and fruitful topic of nonlinear
systems theory. We generalize this approach beyond equilibrium stability
analysis with the aim of characterizing feedback systems whose asymptotic
behavior is low dimensional. We illustrate the theory with a generalization of
the circle criterion for the analysis of multistable and oscillatory Lur'e
feedback systems.
