English

Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs

Systems and Control 2025-09-10 v2 Systems and Control Optimization and Control

Abstract

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.

Keywords

Cite

@article{arxiv.2504.01585,
  title  = {Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs},
  author = {Julius P. J. Krebbekx and Roland Tóth and Amritam Das},
  journal= {arXiv preprint arXiv:2504.01585},
  year   = {2025}
}

Comments

8 pages, accepted for CDC 2025

R2 v1 2026-06-28T22:43:40.424Z