Computable Characterisations of Scaled Relative Graphs of Closed Operators
This work addresses stability analysis for control systems engineers, offering incremental improvements by extending SRG constructions to broader operator classes.
The paper tackled the problem of constructing Scaled Relative Graphs (SRG) for closed linear operators to analyze stability and robustness in multi-input multi-output systems, providing exact and computable tools based on gain computations that apply to both bounded and unbounded operators, with specific applications to linear-time-invariant dynamical systems and state-space models using the Bounded Real Lemma.
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. Furthermore, for the special case of state-space models, we show how the Bounded Real Lemma can be used to construct the SRG.