Analysis of Lur'e dominant systems in the frequency domain
For control theorists, it extends classical nonlinear system analysis to broader dynamical behaviors, though the contribution is incremental.
The paper generalizes frequency domain analysis of Lur'e systems to characterize low-dimensional asymptotic behavior beyond equilibrium stability, providing a generalized circle criterion for multistable and oscillatory systems.
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.