2010
DOI: 10.1016/j.sysconle.2010.07.002
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Non-dissipative boundary feedback for Rayleigh and Timoshenko beams

Abstract: We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

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Cited by 9 publications
(21 citation statements)
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“…(1) It is technically convenient to start with the proof of statement (2). To this end, we show that, for the case when κ 1 = κ 2 = 0, the operator L is dissipative.…”
Section: Proof Of Theorem 24mentioning
confidence: 97%
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“…(1) It is technically convenient to start with the proof of statement (2). To this end, we show that, for the case when κ 1 = κ 2 = 0, the operator L is dissipative.…”
Section: Proof Of Theorem 24mentioning
confidence: 97%
“…(iii) The situation when the combination of two positive control parameters involves one diagonal element of the control matrix (α or β) and one co-diagonal element (κ 1 or κ 2 ) is more complicated. It is proven in statements (2) and (3) of theorem 2.4 that, for two cases when either α > 0, κ 1 > 0 and β = κ 2 = 0 or β > 0, κ 2 > 0 and α = κ 1 = 0, the stability result holds, i.e. the entire spectra of the corresponding operators are located in the open upper half-plane.…”
Section: Introductionmentioning
confidence: 94%
“…Now we replace the free right-end conditions from Eq. (3) with the following boundary feedback control law [2,4]. Define the input and the output as…”
Section: The Initial-boundary Value Problem For the Euler-bernoulli Bmentioning
confidence: 99%
“…Based on the results of [1,2], the dynamics generator has a purely discrete spectrum, whose location on the complex plane is determined by the controls k 1 and k 2 . Having in mind the practical applications of the asymptotic formulas [3][4][5], we discuss the case of k 1 ≥ 0 and k 2 ≥ 0, such that |k 1 | þ |k 2 | . 0 (see Proposition 2).…”
Section: Introductionmentioning
confidence: 99%
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