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We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…

Dynamical Systems · Mathematics 2023-06-13 Lucas Illing , Pierce Ryan , Andreas Amann

We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is…

Dynamical Systems · Mathematics 2015-03-17 Jan Sieber , Matthias Wolfrum , Mark Lichtner , Serhiy Yanchuk

This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…

Optimization and Control · Mathematics 2026-03-03 Matthieu Barreau , Carsten W. Scherer , Frederic Gouaisbaut , Alexandre Seuret

We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…

Analysis of PDEs · Mathematics 2017-02-12 Cristina Pignotti

Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…

Analysis of PDEs · Mathematics 2024-08-07 Marek Kryspin , Janusz Mierczyński

Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…

Systems and Control · Electrical Eng. & Systems 2025-11-12 Tessina H. Scholl

In this paper we investigate the uniform exponential stability of the system $\frac{dx(t)}{dt}=Ax(t)-\rho Bx(t), \; (\rho >0), $ where the unbounded operator $A$ is the infinitesimal generator of a linear $C_0-$semigroup of contractions…

Optimization and Control · Mathematics 2021-11-16 Safae El Alaoui , Mohamed Ouzahra

We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the…

Dynamical Systems · Mathematics 2014-02-05 Timothy Blass , L. A. Romero , J. R. Torczynski

Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$…

Dynamical Systems · Mathematics 2020-12-22 Leonid Berezansky , Elena Braverman

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

Dynamical Systems · Mathematics 2024-02-14 Anatoli Ivanov , Sergiy Shelyag

The problem of p-th moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii…

Dynamical Systems · Mathematics 2016-07-11 Bin Zhou , Weiwei Luo

This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the…

Dynamical Systems · Mathematics 2023-02-28 Sébastien Fueyo , Guilherme Mazanti , Islam Boussaada , Yacine Chitour , Silviu-Iulian Niculescu

The $\mu$-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel $\mu$-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is…

Dynamical Systems · Mathematics 2022-06-22 Mustafa Aydin , Nazim I. Mahmudov

We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive {\tau} for which the corresponding discrete time…

Optimization and Control · Mathematics 2014-07-16 Vladimir Yu. Protasov , Raphael M. Jungers

For a nonlinear equation with several variable delays $$ \dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a…

Dynamical Systems · Mathematics 2016-06-10 Leonid Berezansky , Elena Braverman

This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…

Dynamical Systems · Mathematics 2015-06-05 Lenonid Bunimovich , Benjamin Webb

In this note, we shall consider the existence of invariant measures for a class of infinite dimensional stochastic functional differential equations with delay whose driving semigroup is eventually norm continuous. The results obtained are…

Probability · Mathematics 2014-02-11 Kai Liu

In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent…

Dynamical Systems · Mathematics 2015-06-01 Xiwei Liu , Tianping Chen

In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…

Optimization and Control · Mathematics 2024-09-23 David Reber , Benjamin Webb

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic…

Optimization and Control · Mathematics 2016-11-17 Martin S. Andersen , Anders Hansson , Sina Khoshfetrat Pakazad , Anders Rantzer