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We investigate the dynamics of a single breathing localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We show that variation of the delay time and the feedback strength can lead either…

Pattern Formation and Solitons · Physics 2015-06-18 Svetlana V. Gurevich

We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that…

Optimization and Control · Mathematics 2019-11-21 Christophe Zhang

We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it…

Optimization and Control · Mathematics 2022-12-12 Georges Bastin , Jean-Michel Coron , Amaury Hayat

Recently, the problem of boundary stabilization for unstable linear constant-coefficient reaction-diffusion equation on N-balls has been solved by means of the backstepping method. However, the extension of this result to spatially-varying…

Optimization and Control · Mathematics 2016-01-11 Rafael Vazquez , Miroslav Krstic

This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…

Optimization and Control · Mathematics 2025-02-24 Haitian Yang , Wen-An Yong

Here we deal with the stabilization problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into…

Optimization and Control · Mathematics 2021-07-19 Ionut Munteanu

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

Optimization and Control · Mathematics 2024-01-22 Dandan Guan , Jie Qi , Mamadou Diagne

In this paper, we address the problem of stabilization in continuous time linear dynamical systems using state feedback when compressive sampling techniques are used for state measurement and reconstruction. In [5], we had introduced the…

Optimization and Control · Mathematics 2011-10-18 Kang Kang , Sourabh Bhattacharya , Tamer Basar

This paper addresses the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs with delayed boundary measurement. The output takes the form of a either Dirichlet or Neumann trace. The output delay can be arbitrarily…

Optimization and Control · Mathematics 2021-06-28 Hugo Lhachemi , Christophe Prieur

Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…

Optimization and Control · Mathematics 2023-09-04 Ala' Alalabi , Kirsten Morris

Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…

Analysis of PDEs · Mathematics 2024-11-04 Thi Lien Nguyen , Bao Quoc Tang

This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and actuated input. The observed data are composed of tuples of current state, input, and the next state's interval…

Optimization and Control · Mathematics 2023-09-26 Jared Miller , Jian Zheng , Mario Sznaier , Chris Hixenbaugh

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…

Optimization and Control · Mathematics 2008-06-23 Luca Scardovi , Naomi Leonard , Rodolphe Sepulchre

We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical…

Optimization and Control · Mathematics 2024-12-30 Varga Kalantarov , Türker Özsarı , Kemal Cem Yılmaz

The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…

Systems and Control · Electrical Eng. & Systems 2020-01-17 Andrea Cristofaro , Francesco Ferrante

In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…

Optimization and Control · Mathematics 2026-04-30 Picchiotti Flavio , Thiago Alves Lima , Girard Antoine

We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…

Analysis of PDEs · Mathematics 2024-10-30 Vincent Bansaye , Ayman Moussa , Felipe Muñoz-Hernández

This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…

Optimization and Control · Mathematics 2023-10-19 Constantinos Kitsos , Emilia Fridman

This paper studies the stabilization for a kind of linear and impulse control systems in finite-dimensional spaces, where impulse instants appear periodically. We present several characterizations on the stabilization; show how to design…

Optimization and Control · Mathematics 2019-07-11 Shulin Qin , Gengsheng Wang , Huaiqiang Yu

This paper studies the design of a finite-dimensional output feedback controller for the stabilization of a reaction-diffusion equation in the presence of a sector nonlinearity in the boundary input. Due to the input nonlinearity, classical…

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