Related papers: Deductive Stability Proofs for Ordinary Differenti…
A discrete-time linear dynamical system (LDS) is given by an update matrix $M \in \mathbb{R}^{d\times d}$, and has the trajectories $\langle s, Ms, M^2s, \ldots \rangle$ for $s \in \mathbb{R}^d$. Reachability-type decision problems of…
Neural Ordinary Differential Equations (NODEs) are a novel neural architecture, built around initial value problems with learned dynamics which are solved during inference. Thought to be inherently more robust against adversarial…
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
We introduce OS-net (Orbitally Stable neural NETworks), a new family of neural network architectures specifically designed for periodic dynamical data. OS-net is a special case of Neural Ordinary Differential Equations (NODEs) and takes…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…
Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a…
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
This article introduces a relatively complete proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform…
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs…
Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…