Displaying similar documents to “Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach”

Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss...

Stabilization of Timoshenko Beam by Means of Pointwise Controls

Gen-Qi Xu, Siu Pang Yung (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build...

Exact controllability of shells in minimal time

Paola Loreti (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove an exact controllability result for thin cups using the Fourier method and recent improvements of Ingham type theorems, given in a previous paper [2].

Controlling a non-homogeneous Timoshenko beam with the aid of the torque

Grigory M. Sklyar, Grzegorz Szkibiel (2013)

International Journal of Applied Mathematics and Computer Science

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Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they...

Stabilization of Timoshenko beam by means of pointwise controls

Gen-Qi Xu, Siu Pang Yung (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build...

Exact null controllability of structurally damped and thermo-elastic parabolic models

Irena Lasiecka, Roberto Triggiani (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We show exact null-controllability for two models of non-classical, parabolic partial differential equations with distributed control: (i) second-order structurally damped equations, except for a limit case, where exact null controllability fails; and (ii) thermo-elastic equations with hinged boundary conditions. In both cases, the problem is solved by duality.