Scaled Relative Graph Analysis of General Interconnections of SISO Nonlinear Systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915402623221760 |
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| 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 limits its applicability in analyzing practical nonlinear systems. We overcome this pitfall by introducing a novel reformulation of the SRG of a linear time-invariant operator and combining the SRG with the Nyquist criterion. The result is a theorem that can be used to assess stability and $L_2$-gain performance for general interconnections of nonlinear dynamic systems. We provide practical calculation results for canonical interconnections and apply our result to Lur'e systems to obtain a generalization of the celebrated circle criterion, which deals with broader class of nonlinearities, and we derive (incremental) $L_2$-gain performance bounds. We illustrate the power of the new approach on the analysis of several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaled Relative Graph Analysis of General Interconnections of SISO Nonlinear Systems 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 limits its applicability in analyzing practical nonlinear systems. We overcome this pitfall by introducing a novel reformulation of the SRG of a linear time-invariant operator and combining the SRG with the Nyquist criterion. The result is a theorem that can be used to assess stability and $L_2$-gain performance for general interconnections of nonlinear dynamic systems. We provide practical calculation results for canonical interconnections and apply our result to Lur'e systems to obtain a generalization of the celebrated circle criterion, which deals with broader class of nonlinearities, and we derive (incremental) $L_2$-gain performance bounds. We illustrate the power of the new approach on the analysis of several examples. |
| title | Scaled Relative Graph Analysis of General Interconnections of SISO Nonlinear Systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2507.15564 |