English
Related papers

Related papers: Large-Time Asymptotics for Hyperbolic Systems with…

200 papers

The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…

Optimization and Control · Mathematics 2024-04-23 Michael Herty , Hicham Kouhkouh

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…

Optimization and Control · Mathematics 2013-11-15 Corentin Briat

Recently, a nonlinear stability theory has been developed for wave trains in reaction-diffusion systems relying on pure $L^\infty$-estimates. In the absence of localization of perturbations, it exploits diffusive decay caused by smoothing…

Analysis of PDEs · Mathematics 2024-10-24 Joannis Alexopoulos , Björn de Rijk

These lectures present the analysis of stability and control of long time behavior of PDE models described by nonlinear evolutions of hyperbolic type. Specific examples of the models under consideration include: (i) nonlinear systems of…

Analysis of PDEs · Mathematics 2012-04-27 Igor Chueshov , Irena Lasiecka

We show that a simple Levi compatibility condition determines stability of WKB solutions to semilinear hyperbolic initial-value problems issued from highly-oscillating initial data with large amplitudes. The compatibility condition involves…

Analysis of PDEs · Mathematics 2015-04-29 Yong Lu , Benjamin Texier

In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…

Optimization and Control · Mathematics 2021-12-01 Andrea Zanelli , Quoc Tran Dinh , Moritz Diehl

In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…

Dynamical Systems · Mathematics 2017-05-31 Nina Xue , Xiong Li

We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…

Optimization and Control · Mathematics 2014-08-25 Matthew M. Peet , Alexandre Seuret

We present the global-in-time existence of strong solutions and its large-time behavior for the Kuramoto-Sakaguchi equation with inertia. The equation describes the evolution of the probability density function for a large ensemble of…

Analysis of PDEs · Mathematics 2018-06-14 Young-Pil Choi , Seung-Yeal Ha , Qinghua Xiao , Yinglong Zhang

We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimensions. However, a reduced system may be unstable, although…

Numerical Analysis · Mathematics 2018-08-14 Roland Pulch

We give the first proof of nonlinear stability for smooth shock profiles of second-order dissipative hyperbolic-hyperbolic systems under the assumption of spectral stability, showing stability of smooth small-amplitude profiles in…

Analysis of PDEs · Mathematics 2025-10-13 Matthias Sroczinski , Kevin Zumbrun

Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous…

Optimization and Control · Mathematics 2020-07-09 Jean-Michel Coron , Hoai-Minh Nguyen

We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…

Dynamical Systems · Mathematics 2016-11-17 A. N. Gorban , I. Yu. Tyukin , H. Nijmeijer

In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time…

Optimization and Control · Mathematics 2025-06-26 Kamal Fenza , Moussa Labbadi , Mohamed Ouzahra

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

Analysis of PDEs · Mathematics 2025-12-10 Irina Kmit , Natalya Lyul'ko

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…

Optimization and Control · Mathematics 2016-11-09 Corentin Briat

Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions,…

Dynamical Systems · Mathematics 2015-07-22 Jun Liu , Andrew R. Teel

We introduce a novel method to investigate the stability of wave packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is non-perturbative. Two separate contributions to the quantum…

Chaotic Dynamics · Physics 2009-11-11 Jens Bolte , Tobias Schwaibold

In this paper we study the stabilization problem of a general class of slow-fast systems with one fast and arbitrarily many slow states. Moreover, the class of systems under study is slowly actuated, meaning that only the slow states are…

Dynamical Systems · Mathematics 2017-10-05 Hildeberto Jardón-Kojakhmetov , Jacquelien M. A. Scherpen

This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability…

Analysis of PDEs · Mathematics 2020-11-19 Fangfang Dou , Masahiro Yamamoto