arXiv subjects

Richard Pates

Publications and source records attributed to Richard Pates.

2 recordsLinked to original sources

arXiv2026

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

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.

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arXiv2026

Computable Characterisations of Scaled Relative Graphs of Closed Operators

The Scaled Relative Graph (SRG) is a promising tool for stability and robustness analysis of multi-input multi-output systems. In this paper, we provide tools for exact and computable constructions of the SRG for closed linear operators, based on maximum and minimum gain computations. The results are suitable for bounded and unbounded operators, and we specify how they can be used to draw SRGs for the typical operators that are used to model linear-time-invariant dynamical systems. For the special case of state-space models, we show how the Bounded Real Lemma can be used to construct the SRG. Furthermore, we give an example of how stability analysis of dynamical systems can be done with SRGs.

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