Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs

Abstract: Scaled Relative Graphs (SRGs) provide a novel graphical frequency domain method for the analysis of nonlinear systems. In this paper, we use the restriction of the SRG to particular input spaces to compute frequency-dependent gain bounds for incrementally stable nonlinear systems. This leads to a nonlinear (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 LTI definitions. We illustrate the power of our method on the analysis of a DC motor with a parasitic nonlinearity, verifying our results in simulations.