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On stabilization of an elastic system by fast-oscillating time-variant feedback

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Abstract

We study a class of elastic systems described by a (hyperbolic) second-order partial differential equation. Our working example is the equation of a vibrating string subject to a destabilizing linear disturbance. Our main goal is to establish conditions for stabilization and asymptotic stabilization of the equilibrium configuration of the string by applying to it fast oscillating controlled force. In the first situation studied we assume that the string is subject to damping; after that we consider the same system without damping. We extend the tools of high-order averaging and of chronological calculus for studying the stability of this distributed parameter system.

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Authors and Affiliations

  1. Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Potugal

    M. I. Caiado

  2. Dipartimento di Matematica per le Decisioni, Università di Firenze, Florence, Italy

    A. V. Sarychev

Authors
  1. M. I. Caiado
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  2. A. V. Sarychev
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Correspondence to M. I. Caiado.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 66, Optimal Control, 2010.

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Caiado, M.I., Sarychev, A.V. On stabilization of an elastic system by fast-oscillating time-variant feedback. J Math Sci 173, 107–121 (2011). https://doi.org/10.1007/s10958-011-0234-9

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  • DOI: https://doi.org/10.1007/s10958-011-0234-9

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