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

Ingham-type inequalities and Riesz bases of divided differences

Sergei Avdonin, William Moran (2001)

International Journal of Applied Mathematics and Computer Science

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We study linear combinations of exponentials e^{iλ_nt} , λ_n ∈ Λ in the case where the distance between some points λ_n tends to zero. We suppose that the sequence Λ is a finite union of uniformly discrete sequences. In (Avdonin and Ivanov, 2001), necessary and sufficient conditions were given for the family of divided differences of exponentials to form a Riesz basis in space L^2 (0,T). Here we prove that if the upper uniform density of Λ is less than T/(2π), the family of divided differences...

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

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2006)

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...

Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity

Weijiu Liu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer to a related open question raised by Alabau...