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Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.

Functional Analysis · Mathematics 2013-03-13 András Bátkai

This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the…

Optimization and Control · Mathematics 2022-07-13 Hugo Lhachemi , Christophe Prieur

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Without imposing any hypotheses on the structural properties of the damping term, we identify logarithmic decay of solutions with growing…

Analysis of PDEs · Mathematics 2020-04-23 Kaïs Ammari , Fathi Hassine , Luc Robbiano

Vibrational structures are susceptible to catastrophic failures or structural damages when external forces induce resonances or repeated unwanted oscillations. One common mitigation strategy is to use dampers to suppress these disturbances.…

Optimization and Control · Mathematics 2025-09-09 Petar Mlinarić , Serkan Gugercin , Zoran Tomljanović

The presence of a delay in a thermoelastic system destroys the well-posedness and the stabilizing effect of the heat conduction. To avoid this problem we add to the system, at the delayed equation, a Kelvin-Voigt damping. In this note we…

Analysis of PDEs · Mathematics 2022-12-20 Smain Moulay Khatir , Farhat Shel

This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…

Optimization and Control · Mathematics 2012-12-05 Iasson Karafyllis , Miroslav Krstic

We obtain a novel interior control result for wave equations on time dependent domains. This is done by deriving a suitable Carleman estimate and proving the corresponding observability inequality. We consider the wave equation with time…

Analysis of PDEs · Mathematics 2022-07-27 Vaibhav Kumar Jena

The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The…

Classical Analysis and ODEs · Mathematics 2008-12-31 Fatihcan M. Atay

In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping…

Analysis of PDEs · Mathematics 2017-06-02 Varga K. Kalantarov , Edriss S. Titi

We demonstrate the first successful non-invasive stabilisation of nonlinear travelling waves in a straight cylindrical pipe using time-delayed feedback control (TDF) working in various symmetry subspaces. By using an approximate linear…

Fluid Dynamics · Physics 2025-02-19 Tatsuya Yasuda , Dan Lucas

In this paper, we investigate the direct and indirect stability of locally coupled wave equations with local viscous damping on cylindrical and non-regular domains without any geometric control condition. If only one equation is damped, we…

Analysis of PDEs · Mathematics 2021-11-30 Mohammad Akil , Haidar Badawi , Serge Nicaise , Virginie Régnier

We present a frequency domain based $H_\infty$-control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation, where controllers are constrained to be physically…

Optimization and Control · Mathematics 2019-05-17 Pierre Apkarian , Dominikus Noll

It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from…

Optimization and Control · Mathematics 2020-11-30 Behzad Azmi , Karl Kunisch , Sérgio S. Rodrigues

We study the problem of stabilization for the acoustic system with a spatially distributed damping. With imposing hypothesis on the structural properties of the damping term, we identify exponential decay of solutions with growing time.

Analysis of PDEs · Mathematics 2023-02-07 Kaïs Ammari , Fathi Hassine , Luc Robbiano

This paper discusses the robustness of the constant-delay predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based…

Optimization and Control · Mathematics 2019-08-29 Hugo Lhachemi , Christophe Prieur , Robert Shorten

Hill's equation is a common model of a time-periodic system that can undergo parametric resonance for certain choices of system parameters. For most kinds of parametric forcing, stable regions in its two-dimensional parameter space need to…

Dynamical Systems · Mathematics 2024-08-19 Karthik Chikmagalur , Bassam Bamieh

Results of stabilization for the higher order of the Kadomtsev-Petviashvili equation are presented in this manuscript. Precisely, we prove with two different approaches that under the presence of a damping mechanism and an internal delay…

Analysis of PDEs · Mathematics 2022-12-29 Roberto de A. Capistrano-Filho , Victor H. Gonzalez Martinez , Juan Ricardo Muñoz

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…

Optimization and Control · Mathematics 2026-03-20 Guangqiang Lan , Fansai Meng

This paper addresses the problem of stabilization of $1$-D parabolic equations with destabilizing terms and Dirichlet boundary disturbances. By using the method of backstepping and the technique of splitting, a boundary feedback controller…

Optimization and Control · Mathematics 2024-07-23 Jun Zheng , Guchuan Zhu

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