Analysis of Lur'e dominant systems in the frequency domain

TL;DR

This paper extends frequency domain analysis of LTI systems with nonlinear feedback to characterize systems with low-dimensional asymptotic behavior, including multistability and oscillations, using a generalized circle criterion.

Contribution

It generalizes classical frequency domain methods to analyze complex Lur'e systems beyond equilibrium stability, focusing on asymptotic dynamics.

Findings

Generalized circle criterion for multistable and oscillatory systems

Characterization of low-dimensional asymptotic behavior

Extension of frequency domain analysis beyond equilibrium stability

Abstract

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.