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Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…

Dynamical Systems · Mathematics 2022-06-14 Leonid Berezansky , Elena Braverman

We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a…

Analysis of PDEs · Mathematics 2014-07-18 Serge Nicaise , Cristina Pignotti

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

We describe the asymptotic behaviour and the stability properties of the solutions to a second order rational difference equation.

Dynamical Systems · Mathematics 2009-05-25 Ignacio Bajo , Eduardo Liz

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…

Dynamical Systems · Mathematics 2026-03-12 Pragati Dutta , Sachin Bhalekar

In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on…

Analysis of PDEs · Mathematics 2018-02-06 M. F. G. Palma , C. R. da Luz

We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the…

Analysis of PDEs · Mathematics 2013-02-19 Thomas Roche , Riccarda Rossi , Ulisse Stefanelli

We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact…

Analysis of PDEs · Mathematics 2018-02-27 Bernhard Haak , Duc-Trung Hoang , El-Maati Ouhabaz

We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the…

Numerical Analysis · Mathematics 2020-11-18 Petr N. Vabishchevich

Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…

Systems and Control · Electrical Eng. & Systems 2021-10-28 Stefan Wildhagen , Julian Berberich , Matthias Hirche , Frank Allgöwer

We investigate the asymptotic behavior of solutions to a second order differential equation with vanishing damping term, convex potential and regularizing Tikhonov term.

Optimization and Control · Mathematics 2017-12-01 Mounir Elloumi , Ramzi May , Chokri Mnasri

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…

Analysis of PDEs · Mathematics 2020-07-27 Kaïs Ammari , Boumediène Chentouf , Nejib Smaoui

In this paper we characterize the output feedback stabilization of some coupled systems with delay. The proof of the main result uses the method introduced in Ammari and Tucsnak \cite{at} where the exponential stability for the closed loop…

Analysis of PDEs · Mathematics 2010-10-19 E. M. Ait Benhassi , K. Ammari , S. Boulite , L. Maniar

In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…

Analysis of PDEs · Mathematics 2016-11-07 Yacine Chitour , Guilherme Mazanti , Mario Sigalotti

The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…

Analysis of PDEs · Mathematics 2017-04-13 Wolf-Jürgen Beyn , Denny Otten , Jens Rottmann-Matthes

In this paper, by means of the Riesz basis approach, we study the stability of a weakly damped system of two second order evolution equations coupled through the velocities. If the fractional order damping becomes viscous and the waves…

Analysis of PDEs · Mathematics 2018-08-31 Farah Abdallah , Yacine Chitour , Mouhammad Ghader , Ali Wehbe

We consider initial-boundary-value problems for a class of nonlinear third order equations having non-autonomous forcing terms and get new asymptotic stability results by means of the Liapunov second method. The class includes equations…

Mathematical Physics · Physics 2012-09-28 Armando D'Anna , Gaetano Fiore

We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…

Analysis of PDEs · Mathematics 2020-10-20 Kaïs Ammari , Fathi Hassine , Luc Robbiano

We consider abstract evolution equations with a nonlinear term depending on the state and on delayed states. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains…

Analysis of PDEs · Mathematics 2017-05-11 Serge Nicaise , Cristina Pignotti

In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…

Classical Analysis and ODEs · Mathematics 2010-07-12 Basak Karpuz