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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…
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…
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…
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…
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,…
The Scaled Relative Graph (SRG) is a geometric tool that maps the action of a multi-valued nonlinear operator onto the 2D plane, used to analyze the convergence of a wide range of iterative methods. As the SRG includes the spectrum for…
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…
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…
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…
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…
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…
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…
We introduce a novel approach to feedback stability analysis for linear time-invariant (LTI) systems, overcoming the limitations of the sectoriality assumption in the small phase theorem. While phase analysis for single-input single-output…
The scaled relative graph (SRG) is a powerful graphical tool for analyzing the properties of operators, by mapping their graph onto the complex plane. In this work, we study the SRG of two classes of nonmonotone operators, namely the…
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…
The paper extends the Scaled Relative Graph (SRG) framework of Ryu, Hannah, and Yin from Hilbert spaces to normed spaces. Our extension replaces the inner product with a regular pairing, whose asymmetry gives rise to directional angles and,…
The scaled relative graph (SRG) of an operator is a subset of the complex plane. It captures several salient features of an operator, such as contractiveness, and can be used to reveal the geometric nature of many of the inequality based…
Scaled Relative Graphs (SRGs) provide an intuitive graphical frequency-domain method for the analysis of Nonlinear (NL) systems, generalizing the Nyquist diagram. In this paper, we develop a method for computing $L_2$-gain bounds for Lur'e…
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…
Scaled graphs offer a graphical tool for analysis of nonlinear feedback systems. Although recently substantial progress has been made in scaled graph analysis, at present their use in multivariable feedback systems is limited by…