Journal ArticleDOI
Feedback stabilization of a class of evolution equations with delay
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TLDR
In this article, Ammari and Tucsnak characterized the stabilization of some delay systems using the method introduced in Ammaris and Tucnamak (ESAIM COCV 6:361-386, 2001) where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system.Abstract:
In this paper, we characterize the stabilization of some delay systems. The proof of the main result uses the method introduced in Ammari and Tucsnak (ESAIM COCV 6:361–386, 2001) where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system.read more
Citations
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Journal ArticleDOI
Stabilization of second order evolution equations with unbounded feedback with delay
Serge Nicaise,Julie Valein +1 more
TL;DR: In this paper, abstract second order evolution equations with unbounded feedback with delay are considered and sufficient and explicit conditions are derived that guarantee the exponential or polynomial stability of these equations.
Journal ArticleDOI
Feedback boundary stabilization of wave equations with interior delay
TL;DR: In this article, the authors considered a boundary stabilization problem for the wave equation with interior delay and proved an exponential stability result under some geometric condition, based on an identity with multipliers that allows them to obtain a uniform decay estimate for a suitable Lyapunov functional.
Journal ArticleDOI
Stabilisation of Timoshenko beam system with delay in the boundary control
Genqi Xu,Hong Xia Wang +1 more
TL;DR: A new dynamic feedback control law is given that makes the system exponential stabilisation ∀τ > 0 provided that |αj| ≠ |βj|(j = 1, 2) and the result is proved via test of exact observability of the system.
Journal ArticleDOI
Stabilization of an Euler–Bernoulli beam with input delay in the boundary control ☆
Ying Feng Shang,Genqi Xu +1 more
TL;DR: A dynamic controller is designed that makes the system stabilize exponentially for any α = 0 and τ > 0 and discusses the stability of the system for | α | = | β | .
Journal ArticleDOI
An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay
TL;DR: In this paper, the authors consider a one-dimensional linear thermoelastic system with a delay, where the heat flux is given by Cattaneo's law and prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary
TL;DR: For the observation or control of solutions of second-order hyperbolic equation in this paper, Ralston's construction of localized states [Comm. Pure Appl. Math, 22 (1969), pp.
Book
Exact controllability and stabilization: The multiplier method
TL;DR: Linear Evolutionary Problems Hidden Regularity Weak Solutions Uniqueness Theorems Exact Controllability Hilbert Uniqueness Method Nonlinear Stabilization Internal Stabilisation of Korteweg-de Vries Equation as discussed by the authors.
Journal ArticleDOI
Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
Serge Nicaise,Cristina Pignotti +1 more
TL;DR: This paper considers the wave equation with a delayed velocity term and mixed Dirichlet-Neumann boundary condition and proves exponential stability of the solution under suitable assumptions.
Journal ArticleDOI
An example on the effect of time delays in boundary feedback stabilization of wave equations
TL;DR: In this article, the erect of time delays in boundary feedback stabilization schemes for wave equations is studied and the question is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays.
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