Related papers: Using asymptotics for efficient stability determin…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…
In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…
We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
This paper is concerned with incremental stability properties of nonlinear systems. We propose conditions to compute an upper bound on the incremental L2-gain and to assess incremental asymptotic stability of piecewise-affine (PWA) systems.…
As the use of machine learning in high impact domains becomes widespread, the importance of evaluating safety has increased. An important aspect of this is evaluating how robust a model is to changes in setting or population, which…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
The robustness of the stability properties of dynamical systems in the presence of unknown/adversarial perturbations to system parameters is a desirable property. In this paper, we present methods to efficiently compute and improve the…
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…
We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…
Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits…