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We use the recently introduced concept of a Scaled Relative Graph (SRG) to develop a graphical analysis of input-output properties of feedback systems. The SRG of a nonlinear operator generalizes the Nyquist diagram of an LTI system. In the…

Systems and Control · Electrical Eng. & Systems 2024-10-28 Thomas Chaffey , Fulvio Forni , Rodolphe Sepulchre

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems, where Linear Time-Invariant (LTI) systems are the fundamental building block. To analyze feedback loops with unstable LTI…

Systems and Control · Electrical Eng. & Systems 2025-11-24 Julius P. J. Krebbekx , Eder Baron-Prada , Roland Tóth , Amritam Das

This paper presents a novel approach to stability analysis for grid-connected converters utilizing Scaled Relative Graphs (SRG). Our method effectively decouples grid and converter dynamics, thereby establishing a comprehensive and…

Systems and Control · Electrical Eng. & Systems 2026-01-23 Eder Baron-Prada , Adolfo Anta , Florian Dörfler

This paper proposes a frequency-wise approach for stability analysis of multi-input, multi-output (MIMO) Linear Time-Invariant (LTI) feedback systems through Scaled Relative Graphs (SRGs). Unlike traditional methods, such as the Generalized…

Systems and Control · Electrical Eng. & Systems 2026-01-26 Eder Baron-Prada , Alberto Padoan , Adolfo Anta , Florian Dörfler

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from a pitfall that limits its applicability in analyzing…

Systems and Control · Electrical Eng. & Systems 2025-07-22 Julius P. J. Krebbekx , Roland Tóth , Amritam Das

Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints…

Optimization and Control · Mathematics 2026-04-03 Timo de Groot , Tom Oomen , W. P. M. H. Heemels , Sebastiaan van den Eijnden

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of Nonlinear (NL) systems. In this paper, we restrict the SRG to particular input spaces to compute frequency-dependent incremental gain bounds…

Systems and Control · Electrical Eng. & Systems 2025-09-10 Julius P. J. Krebbekx , Roland Tóth , Amritam Das

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,…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Talitha Nauta , Richard Pates

In this paper, we utilize a variant of the scaled relative graph (SRG), referred to as the $\theta$-symmetric SRG, to develop a graphical stability criterion for the feedback interconnection of a cascade of systems. A crucial…

Systems and Control · Electrical Eng. & Systems 2025-10-09 Xiaokan Yang , Ding Zhang , Wei Chen , Li Qiu

Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconnection to have finite incremental gain, which generalizes the…

Dynamical Systems · Mathematics 2022-03-29 Thomas Chaffey

The Scaled Relative Graph (SRG) is a generalization of the Nyquist diagram that may be plotted for nonlinear operators, and allows nonlinear robustness margins to be defined graphically. This abstract explores techniques for shaping the SRG…

Systems and Control · Electrical Eng. & Systems 2022-08-10 Thomas Chaffey , Fulvio Forni , Rodolphe Sepulchre

Scaled graphs (SGs) offer a geometric framework for feedback stability analysis. This paper develops containment conditions for SGs within multiplier-defined regions, addressing both circular and conic geometries. For circular regions, we…

Optimization and Control · Mathematics 2026-04-08 Eder Baron-Prada , Julius P. J. Krebbekx , Adolfo Anta , Florian Dörfler

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. There have been recent efforts to generalize SRG analysis to Multiple-Input Multiple-Output (MIMO) systems. However,…

Systems and Control · Electrical Eng. & Systems 2026-04-20 Julius P. J. Krebbekx , Roland Tóth , Amritam Das

We introduce a generalization of the scaled relative graph (SRG) to pairs of operators, enabling the visualization of their relative incremental properties. This novel SRG framework provides the geometric counterpart for the study of…

Optimization and Control · Mathematics 2025-11-26 Jan Quan , Alexander Bodard , Konstantinos Oikonomidis , Panagiotis Patrinos

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from a pitfall that limit its applicability in analyzing practical…

Systems and Control · Electrical Eng. & Systems 2025-04-14 Julius P. J. Krebbekx , Roland Tóth , Amritam Das

We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…

Optimization and Control · Mathematics 2023-03-01 Lassi Paunonen

This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…

Systems and Control · Electrical Eng. & Systems 2021-01-07 Lei Wang , Christopher M. Kellett

Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in…

Optimization and Control · Mathematics 2025-07-14 Timo de Groot , Maurice heemels , Sebastiaan van den Eijnden

Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output…

Systems and Control · Electrical Eng. & Systems 2021-10-08 Thomas Chaffey , Fulvio Forni , Rodolphe Sepulchre

Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and…

Optimization and Control · Mathematics 2021-06-17 Ernest K. Ryu , Robert Hannah , Wotao Yin
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