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Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…

Dynamical Systems · Mathematics 2026-01-13 Mark A. Pinsky

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…

Artificial Intelligence · Computer Science 2024-09-27 Thibault Monsel , Onofrio Semeraro , Lionel Mathelin , Guillaume Charpiat

The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…

Chaotic Dynamics · Physics 2019-10-31 Hendrik Wernecke , Bulcsú Sándor , Claudius Gros

In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…

Analysis of PDEs · Mathematics 2014-01-23 Denys Khusainov , Michael Pokojovy , Elvin Azizbayov

This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable,…

Dynamical Systems · Mathematics 2026-05-22 Sachin Bhalekar

We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop…

Optimization and Control · Mathematics 2014-01-09 R. M. Jungers , A. D'Innocenzo , M. D. Di Benedetto

A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…

Dynamical Systems · Mathematics 2024-08-14 Anatoli Ivanov , Bernhard Lani-Wayda , Sergiy Shelyag

We present a delay-compensating control method that transforms exponentially stabilizing controllers for an undelayed system into a sample-based predictive controller with numerical integration. Our method handles both first-order and…

Systems and Control · Electrical Eng. & Systems 2020-10-01 Xichen Shi , Michael O'Connell , Soon-Jo Chung

The oscillatory behavior of the solutions to a differential equation with several non-monotone delay arguments and non-negative coefficients is studied. A new sufficient oscillation condition, involving lim sup, is obtained. An example…

Classical Analysis and ODEs · Mathematics 2017-03-14 H. Akca , G. E. Chatzarakis , I. P. Stavroulakis

In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin…

Probability · Mathematics 2021-09-07 T. C. Son , N. T. Dung , N. V. Tan , T. M. Cuong , H. T. P. Thao , P. D. Tung

We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic,…

Optimization and Control · Mathematics 2010-09-10 Hao Lu , Michael Di Loreto , Damien Eberard , Jean-Pierre Simon

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast…

Optimization and Control · Mathematics 2012-07-24 Raphael M. Jungers , Alessandro D'Innocenzo , Maria D. Di Benedetto

This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…

Dynamical Systems · Mathematics 2007-05-23 Matthew M. Peet

Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…

Dynamical Systems · Mathematics 2015-05-20 Eoin Devane , Ioannis Lestas

The location of roots of the characteristic equation of a linear delay differential equation (DDE) determines the stability of the linear DDE. However, by its transcendency, there is no general criterion on the contained parameters for the…

Dynamical Systems · Mathematics 2022-06-29 Junya Nishiguchi

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…

Classical Analysis and ODEs · Mathematics 2013-10-01 M. De la Sen

This paper focuses on consensus problems for high-order, linear multi-agent systems. Undirected communication topologies and fixed, uniform communication time delay are taken into account. This class of problems has been widely study in the…

Optimization and Control · Mathematics 2016-05-06 Rudy Cepeda-Gomez

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

Optimization and Control · Mathematics 2013-12-30 S. Damak , M. Di Loreto , W. Lombardi , V Andrieu

This paper presents the analysis of the stability properties of PID controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to…

Optimization and Control · Mathematics 2020-09-08 Pieter Appeltans , Silviu-Iulian Niculescu , Wim Michiels

This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…

Dynamical Systems · Mathematics 2026-05-07 Pragati Dutta , Sachin Bhalekar