Computing Scaled Relative Graphs of Discrete-time LTI Systems from Data

Abstract

Graphical methods for system analysis have played a central role in control theory. The Scaled Relative Graph (SRG) has recently emerged as a useful tool for stability analysis of feedback interconnections. In this paper, we further extend its applicability by showing how the SRG of a discrete-time linear-time-invariant (LTI) system can be computed exactly from its state-space representation using linear matrix inequalities. We additionally propose a fully data-driven approach where we demonstrate how to compute the SRG exclusively from input-output data. Furthermore, we introduce a robust version of the SRG, which can be computed from noisy data trajectories and contains the SRG of the actual system.