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We study sufficient conditions for stability and recurrence in a class of singularly perturbed stochastic hybrid dynamical systems. The systems considered combine multi-time-scale deterministic continuous-time dynamics, modeled by…
This paper demonstrates the concept of probabilistic stability assessment on large-signal stability in the use case of short circuits in an active distribution grid. Here, the concept of survivability is applied, which extends classical…
We consider small perturbations of expanding maps induced by skew-product mappings whose base dynamics are not invertible necessarily. Adopting a previously developed perturbative spectral approach, we show stability of the densities of the…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
Power electronic devices such as HVDC and FACTS can be used to improve the damping of poorly damped inter-area modes in large power systems. This involves the use of wide-area feedback signals, which are transmitted via communication…
An initial-boundary value problem for the $n$-dimensional wave equation is considered. A three-level explicit in time and conditionally stable 4th-order compact scheme constructed recently for $n=2$ and the square mesh is generalized to the…
We analyze the stability of recurrent networks, specifically, reservoir computing models during training by evaluating the eigenvalue spectra of the reservoir dynamics. To circumvent the instability arising in examining a closed loop…
The design of large complex wave systems (filters, networks, vacuum-electronic devices, metamaterials, smart radio environments, etc.) requires repeated evaluations of the scattering parameters resulting from complex connections between…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
The unexpected emerging stability of a time-modulated magnetic guide, realized without external offset fields, is demonstrated. We found a steady periodic solution around which the nonlinear dynamics is linearized. To investigate the…
Realistic multiport interferometers (beamsplitter meshes) are sensitive to component imperfections, and this sensitivity increases with size. Self-configuration techniques can be employed to correct these imperfections, but not all…
Reliable and secure operation of power systems becomes increasingly challenging as the share of volatile generation rises, leading to largely changing dynamics. Typically, the architecture and structure of controllers in power systems, such…
This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…
This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…
Renewable-driven microgrids dominated by grid-forming (GFM) converters are subject to persistent power fluctuations, making equilibrium-known stability assessments restrictive. This paper develops an equilibrium-free contraction stability…
This paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process. We show that the mean stability of such a switched system is characterized by the…
Power distribution systems are becoming much more active with increased penetration of distributed energy resources. Because of the intermittent nature of these resources, the stability of distribution systems under large disturbances and…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
This paper is focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability,…