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Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs

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arxiv 2504.01585 v2 pith:HUQZKRED submitted 2025-04-02 eess.SY cs.SYmath.OC

Julius P. J. Krebbekx , Roland Tóth , Amritam Das This is my paper · ORCID
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keywords analysisnonlinearbandwidthbodegraphsmethodrelativescaled
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Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of Nonlinear (NL) systems. In this paper, we restrict the SRG to particular input spaces to compute frequency-dependent incremental gain bounds for nonlinear systems. This leads to a NL generalization of the Bode diagram, where the sinusoidal, harmonic, and subharmonic inputs are considered separately. When applied to the analysis of the NL loop transfer and sensitivity, we define a notion of bandwidth for both the open-loop and closed-loop, compatible with the Linear Time-Invariant (LTI) definitions. We illustrate the power of our method on the analysis of a DC motor with a parasitic nonlinearity and verify our results in simulations.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion

    eess.SY 2024-11 conditional novelty 7.0 of 10

    A Nyquist-aware extended Scaled Relative Graph lets SRG analysis handle unstable plants and yields a generalized circle criterion with L2-gain bounds.

  2. Scaled Relative Graph Analysis of General Interconnections of SISO Nonlinear Systems

    eess.SY 2025-07 reject novelty 6.0 of 10

    The authors introduce an extended Scaled Relative Graph that includes Nyquist encirclement data, enabling stability and L2-gain analysis of feedback interconnections with unstable linear components.

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