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The largest eigenvalue of a network's adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically…
A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…
Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous…
In this paper, a novel approach based on robust stability concepts and tools is introduced to evaluate the unconditional stability of microwave active $\textit{n}$-port devices. An efficient calculation of the Structured Singular Value of…
Motivated by recent progress on the scaling behavior of entanglement entropy, we study the scaling behavior of the number of clusters crossing the boundary between two subsystems for several classical statistical models in two dimension.…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
In this paper, we consider nonlinear control systems subject to bounded disturbances and to both state and input constraints. We introduce the definition of robust admissible set - the set of all initial states from which the state and…
A systematic approach to assess the linear stability of Alfv\'en eigenmodes in the presence of fusion-born alpha particles is described. Because experimental results for ITER are not available yet, it is not known beforehand which Alfv\'en…
Modern power system is undergoing a paradigm shift from the synchronous generators-based system to the power electronics converters-dominated system. With the high penetration of converters, serious stability problems are provoked,…
Assessing small-signal stability of power systems composed of thousands of interacting generators is a computationally challenging task. To reduce the computational burden, this paper introduces a novel condition to assess and certify…
We study vortex clustering in type II Superconductors. We demonstrate that the ``second peak'' observed in magnetisation loops may be a dynamical effect associated with a density driven instability of the vortex system. At the microscopic…
Passivity indices have been widely adopted to derive distributed stability certificates for power systems. Nevertheless, conventional passivity indices remain scalar-valued even for multi-input-multi-output (MIMO) systems, which can…
Virtual inertia is an effective control approach to attenuate sudden voltage changes during transient events in low-inertia DC grids. While methods have been proposed to implement virtual inertia, its impact on DC grid stability in the…
Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…
Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Specifically, several properties of the Gramian submatrices and their inverses --…
In this paper, we consider the problem of tuning the edge weights of a networked system described by linear time-invariant dynamics. We assume that the topology of the underlying network is fixed and that the set of feasible edge weights is…
Learning from two-level voltage source converters, the existing impedance-based stability analyses of modular multilevel converters (MMCs) primarily focus on system modes with finite closed-loop transfer functions, which consider…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
In this paper, we quantify voltage and current phasor-based measurement requirements for the unique estimation of the electric grid topology and admittance parameters. Our approach is underpinned by the concept of a rigidity matrix that has…
As modern power systems continue to evolve into multi-agent, converter-dominated systems that demand reliable, stable, and optimal control architectures within an expandable framework, this paper investigates scalable stability guarantees…