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

TL;DR

This paper introduces methods to compute the Scaled Relative Graph (SRG) of discrete-time LTI systems from both state-space models and input-output data, including a robust version for noisy data, enhancing system analysis tools.

Contribution

It extends SRG applicability by providing exact computation from models and data, and introduces a robust SRG for noisy data scenarios.

Findings

Exact SRG computation from state-space models using LMIs

Data-driven SRG computation from input-output data

Robust SRG that accounts for noisy data trajectories

Abstract

Graphical methods for system analysis have played a central role in control theory. A recently emerging tool in this field is the Scaled Relative Graph (SRG). In this paper, we further extend its applicability by showing how the SRG of discrete-time linear-time-invariant (LTI) systems 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.