Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917982270128128 |
|---|---|
| author | Krebbekx, Julius P. J. Tóth, Roland Das, Amritam |
| author_facet | Krebbekx, Julius P. J. Tóth, Roland Das, Amritam |
| contents | 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) $L_2$-gain performance bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion Krebbekx, Julius P. J. Tóth, Roland Das, Amritam Systems and Control Optimization and Control 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) $L_2$-gain performance bounds. |
| title | Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2411.18318 |