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Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…

Analysis of PDEs · Mathematics 2016-04-26 Björn Augner , Birgit Jacob

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao

In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of various classes of damped nonlinear wave equations. Specifically, stabilization the zero steady state solution of initial boundary value…

Analysis of PDEs · Mathematics 2015-01-06 Varga K. Kalantarov , Edriss S. Titi

This paper deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the…

Analysis of PDEs · Mathematics 2022-10-26 Ismaïla Balogoun , Swann Marx , Franck Plestan

The paper is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c, 0) of the Euler system there is a control which is…

Analysis of PDEs · Mathematics 2011-08-09 Hayk Nersisyan

This paper studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open loop system might…

Optimization and Control · Mathematics 2020-12-29 Hugo Lhachemi , Christophe Prieur

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 is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…

Analysis of PDEs · Mathematics 2025-03-31 Abdelhakim Dahmani , Yacine Chitour , Hoai-Minh Nguyen , Christophe Roman

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

Analysis of PDEs · Mathematics 2021-03-02 Peijun Li , Xiaohua Yao , Yue Zhao

In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…

Analysis of PDEs · Mathematics 2026-02-06 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is…

Optimization and Control · Mathematics 2022-03-25 Yusen Meng , Hongyinping Feng

This paper is concerned with the analysis of a one dimensional wave equation $z_{tt}-z_{xx}=0$ on $[0,1]$ with a Dirichlet condition at $x=0$ and a damping acting at $x=1$ which takes the form $(z_t(t,1),-z_x(t,1))\in\Sigma$ for every…

Analysis of PDEs · Mathematics 2022-02-21 Yacine Chitour , Swann Marx , Guilherme Mazanti

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

This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…

Optimization and Control · Mathematics 2023-09-06 Tian Xia , Giacomo Casadei , Francesco Ferrante , Luca Scardovi

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…

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

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order that that of the nominal…

Dynamical Systems · Mathematics 2011-08-02 M. De La Sen

This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The…

Optimization and Control · Mathematics 2019-04-22 Matthieu Barreau , Alexandre Seuret , Frédéric Gouaisbaut

In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines…

Optimization and Control · Mathematics 2020-10-28 Axel Ringh , Johan Karlsson , Anders Lindquist

In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain…

Analysis of PDEs · Mathematics 2016-02-10 Kaïs Ammari , Stéphane Gerbi

This paper is devoted to the study of the approximate controllability for a one-dimensional wave equation in domains with moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving.…

Optimization and Control · Mathematics 2025-01-14 Isaías Pereira de Jesus