Computing the Hard Scaled Relative Graph of LTI Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912723121471488 |
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| author | Krebbekx, Julius P. J. Baron-Prada, Eder Tóth, Roland Das, Amritam |
| author_facet | Krebbekx, Julius P. J. Baron-Prada, Eder Tóth, Roland Das, Amritam |
| contents | Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems, where Linear Time-Invariant (LTI) systems are the fundamental building block. To analyze feedback loops with unstable LTI components, the hard SRG is required, since it aptly captures the input/output behavior on the extended $L_2$ space. In this paper, we develop a systematic computational method to exactly compute the hard SRG of LTI systems, which may be unstable and contain integrators. We also study its connection to the Nyquist criterion, including the multivariable case, and demonstrate our method on several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing the Hard Scaled Relative Graph of LTI Systems Krebbekx, Julius P. J. Baron-Prada, Eder 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, where Linear Time-Invariant (LTI) systems are the fundamental building block. To analyze feedback loops with unstable LTI components, the hard SRG is required, since it aptly captures the input/output behavior on the extended $L_2$ space. In this paper, we develop a systematic computational method to exactly compute the hard SRG of LTI systems, which may be unstable and contain integrators. We also study its connection to the Nyquist criterion, including the multivariable case, and demonstrate our method on several examples. |
| title | Computing the Hard Scaled Relative Graph of LTI Systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2511.17297 |