Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion
Systems and Control
2025-04-14 v2 Systems and Control
Optimization and Control
Abstract
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from a pitfall that limit its applicability in analyzing practical nonlinear systems. We overcome this pitfall by modifying the SRG of a linear time invariant operator, combining the SRG with the Nyquist criterion, and apply our result to Lur'e systems. We thereby obtain a generalization of the celebrated circle criterion, which deals with a broader class of nonlinearities, and provides (incremental) -gain performance bounds.
Cite
@article{arxiv.2411.18318,
title = {Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion},
author = {Julius P. J. Krebbekx and Roland Tóth and Amritam Das},
journal= {arXiv preprint arXiv:2411.18318},
year = {2025}
}
Comments
6 pages, 5 figures, (to be) presented at the European Control Conference 2025 and published in the corresponding proceedings