Related papers: Exploiting Structure in MIMO Scaled Graph Analysis
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…
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,…
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…
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…
Graph is a useful data structure to model various real life aspects like email communications, co-authorship among researchers, interactions among chemical compounds, and so on. Supporting such real life interactions produce a knowledge…
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,…
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…
Reset systems can overcome fundamental limitations of linear time-invariant control. The recently introduced notion of scaled (relative) graphs provides a promising framework for developing graphical analysis and design tools for reset…
Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph…
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…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…
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…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Large Language Models (LLMs) have shown remarkable capabilities in processing various data structures, including graphs. While previous research has focused on developing textual encoding methods for graph representation, the emergence of…
We propose a frequency-domain approach to dominance analysis for multi-input multi-output (MIMO) linear time-invariant systems. The dominance of a MIMO system is defined to be the number of its poles in the open right half-plane. Our…
Graph-regularized semi-supervised learning has been used effectively for classification when (i) instances are connected through a graph, and (ii) labeled data is scarce. If available, using multiple relations (or graphs) between the…