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Ukrainian Mathematical Journal

, Volume 60, Issue 2, pp 199–210 | Cite as

Localization of the limit set of trajectories of the Euler-Bernoulli equation with control

  • A. L. Zuev
Article

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.

Keywords

Feedback Control Invariance Principle Elastic Beam BERNOULLI Equation Abstract Cauchy Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • A. L. Zuev
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine

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