Related papers: Subspace Method for the Estimation of Large-Scale …
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
In a "structured system" of equations, each equation depends on a specified subset of the variables. In this article, we explore properties common to "almost every" system with a fixed structure and how the properties can be read from the…
In mathematics, a super-resolution problem can be formulated as acquiring high-frequency data from low-frequency measurements. This extrapolation problem in the frequency domain is well-known to be unstable. We propose a model-based…
Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system $\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero is not the…
We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly study the HD 82943 system by employing two sets of the orbital parameters (Mayor et al. 2004;…
We study the stability of explicit Runge-Kutta methods for high order Lagrangian finite element approximation of linear parabolic equations and establish bounds on the largest eigenvalue of the system matrix which determines the largest…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
Higher-dimensional field theory has been applied to explore various issues in recent particle physics such as the gauge hierarchy problem. In order for such approaches to be viable, a crucial ingredient is to fix the sizes of extra…
In this paper, we study the robustness of safety properties of a linear dynamical system with respect to model uncertainties. Our paper involves three parts. In the first part, we provide symbolic (analytical) and numerical (representation…
Building on the development of a Hermite-Legendre analysis of one-dimensional gravitating collisionless systems, we present a technique for determining the steady states of such systems. This provides an important component for…
Hierarchical triple systems play a crucial role in various astrophysical contexts, and therefore the understanding of their stability is important. Traditional empirical stability criteria rely on a threshold value of $Q$, the ratio between…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
The Riccati equation method is used to establish some new stability criteria for systems of two linear first-order ordinary differential equations. It is shown that two of these criteria in the two dimensional case imply the Routh -…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
We investigate positive definiteness, Hurwitz stability and Schur stability of parametric interval matrices. We give a verifiable sufficient condition for positive definiteness of parametric interval matrices with non-linear dependencies.…
This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than that of the ODE. Such a difference of time scales is modeled…
The stability of astrophysical jets in the linear regime is investigated by presenting the methodology to find the growth rates of the various instabilities. We perturb a cylindrical axisymmetric steady jet, linearize the relativistic ideal…
The natural impedance, or dynamic relationship between force and motion, of a human operator can determine the stability of exoskeletons that use interaction-torque feedback to amplify human strength. While human impedance is typically…