Abstract
We investigate a differential equation in a Hilbert space that describes vibrations of the Euler-Bernoulli elastic beam with feedback control. The relative compactness of positive semitrajectories of the considered equation is proved. Constructing a Lyapunov functional in explicit form and using the invariance principle, we obtain representations of limit sets.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 173–182, February, 2008.
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Zuev, A.L. Localization of the limit set of trajectories of the Euler-Bernoulli equation with control. Ukr Math J 60, 199–210 (2008). https://doi.org/10.1007/s11253-008-0052-5
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DOI: https://doi.org/10.1007/s11253-008-0052-5