Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915999312248832 |
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| author | Chen, Chao Khong, Sei Zhen Sepulchre, Rodolphe |
| author_facet | Chen, Chao Khong, Sei Zhen Sepulchre, Rodolphe |
| contents | This article presents input-output stability analysis of nonlinear feedback systems based on the notion of soft and hard scaled relative graphs (SRGs). The soft and hard SRGs acknowledge the distinction between incremental positivity and incremental passivity and reconcile them from a graphical perspective. The essence of our proposed analysis is that the separation of soft SRGs or hard SRGs of two open-loop systems on the complex plane guarantees closed-loop stability. The main results generalize an existing soft SRG separation theorem for bounded open-loop systems which was proved based on interconnection properties of soft SRGs under a chordal assumption. By comparison, our analysis does not require this chordal assumption and applies to possibly unbounded open-loop systems based on their hard SRGs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability Chen, Chao Khong, Sei Zhen Sepulchre, Rodolphe Systems and Control Optimization and Control This article presents input-output stability analysis of nonlinear feedback systems based on the notion of soft and hard scaled relative graphs (SRGs). The soft and hard SRGs acknowledge the distinction between incremental positivity and incremental passivity and reconcile them from a graphical perspective. The essence of our proposed analysis is that the separation of soft SRGs or hard SRGs of two open-loop systems on the complex plane guarantees closed-loop stability. The main results generalize an existing soft SRG separation theorem for bounded open-loop systems which was proved based on interconnection properties of soft SRGs under a chordal assumption. By comparison, our analysis does not require this chordal assumption and applies to possibly unbounded open-loop systems based on their hard SRGs. |
| title | Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2504.14407 |