Computable Characterisations of Scaled Relative Graphs of Closed Operators

2025/11/11 by Nauta, Talitha, Pates, Richard
#51M15 #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Primary 47A05 #Secondary 47A12 #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2511.08420

Abstract

Scaled Relative Graphs (SRGs) provide 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. Furthermore, for the special case of state-space models, we show how the Bounded Real Lemma can be used to construct the SRG.

Citations

• Graphical Analysis of Nonlinear Multivariable Feedback Systems
• A Dissipativity Framework for Constructing Scaled Graphs
• Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability
• Graphical Dominance Analysis for Linear Systems: A Frequency-Domain Approach
• Stability results for MIMO LTI systems via Scaled Relative Graphs
• Mixed Small Gain and Phase Theorem: A new view using Scale Relative Graphs
• Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion
• Scaled graphs for reset control system analysis
• The Scaled Relative Graph of a Linear Operator
• Scaled relative graphs for system analysis
• Scaled Relative Graph of Normal Matrices
• Scaled relative graphs: nonexpansive operators via 2D Euclidean geometry

Cited by

• Graphical Analysis of Nonlinear Multivariable Feedback Systems

Related

• Computing the Hard Scaled Relative Graph of LTI Systems
• Scaled Relative Graph Analysis of General Interconnections of SISO Nonlinear Systems
• Scaled relative graphs for pairs of operators beyond classical monotonicity
• Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion
• The Scaled Relative Graph of a Linear Operator