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Related papers: Boundary feedback stabilization of quasilinear hyp…

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This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer…

Optimization and Control · Mathematics 2022-08-15 Stephan Gerster , Felix Nagel , Aleksey Sikstel , Giuseppe Visconti

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

We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…

Analysis of PDEs · Mathematics 2017-09-29 Martin Gugat , Vincent Perrollaz , Lionel Rosier

This paper deals with mathematical models of continuous crystallization described by hyperbolic systems of partial differential equations coupled with ordinary and integro-differential equations. The considered systems admit nonzero…

Optimization and Control · Mathematics 2022-01-19 Alexander Zuyev , Peter Benner

We introduce a novel Lyapunov function for stabilization of linear Vlasov--Fokker--Planck type equations with stiff source term. Contrary to existing results relying on transport properties to obtain stabilization, we present results based…

Optimization and Control · Mathematics 2020-02-12 Michael Herty , Shi Jin , Yuhua Zhu

Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic…

Optimization and Control · Mathematics 2024-10-02 Martin Gugat

We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…

Analysis of PDEs · Mathematics 2023-06-21 Xixi Fang , Peng Qu , Huimin Yu

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of…

Optimization and Control · Mathematics 2022-05-18 Suha Shreim , Francesco Ferrante , Christophe Prieur

The paper deals with output feedback stabilization of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic PDE…

Analysis of PDEs · Mathematics 2019-01-09 A Terrand-Jeanne , Vincent Andrieu , Valérie Dos Santos Martins , C. -Z Xu

In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound…

Quantum Physics · Physics 2019-02-12 Weichao Liang , Nina H. Amini , Paolo Mason

In this work, we investigate the exponential stability of the viscous Saint-Venant equations by adding to the standard hyperbolic Saint-Venant equations a viscosity term coming from the higher order approximation of the Saint-Venant…

Analysis of PDEs · Mathematics 2026-03-09 Amaury Hayat , Nathan Lichtlé

We propose a Bayesian framework for feedback boundary control for hyperbolic balance laws. The method propagates a probability distribution over feedback parameters by using Lyapunov decay estimates as a likelihood. In the linear setting,…

Numerical Analysis · Mathematics 2026-02-03 Markus Bambach , Shaoshuai Chu , Michael Herty , Yunong Lin

In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov function in $ L^2- $norm is considered and discretised to…

Optimization and Control · Mathematics 2020-06-05 Gediyon Yemane Weldegiyorgis , Mapundi Kondwani Banda

This paper provides global exponential stabilization results by means of boundary feedback control for 1-D nonlinear unstable reaction-diffusion Partial Differential Equations (PDEs) with nonlinearities of superlinear growth. The class of…

Optimization and Control · Mathematics 2019-03-26 Iasson Karafyllis , Miroslav Krstic

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general…

Optimization and Control · Mathematics 2020-07-07 Andrii Mironchenko , Christophe Prieur , Fabian Wirth

In this work we address the problem of boundary feedback stabilization for a geometrically exact shearable beam, allowing for large deflections and rotations and small strains. The corresponding mathematical model may be written in terms of…

Analysis of PDEs · Mathematics 2020-08-27 Charlotte Rodriguez , Günter Leugering

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time…

Optimization and Control · Mathematics 2020-05-28 Jean-Michel Coron , Hoai-Minh Nguyen

This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular…

Analysis of PDEs · Mathematics 2025-09-25 Nangao Zhang

This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and initial data. Building on the finite volume discretization…

Numerical Analysis · Mathematics 2025-10-10 Shaoshuai Chu , Michael Herty , Alexander Kurganov

This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…

Dynamical Systems · Mathematics 2013-05-17 Martin Meyries , Jens D. M. Rademacher , Eric Siero