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Equivalence between exponential stabilization and boundary observability for piezoelectric beams with magnetic effect

  • A. J. A. RamosEmail author
  • M. M. Freitas
  • D. S. AlmeidaJr.
  • S. S. Jesus
  • T. R. S. Moura
Article
  • 6 Downloads

Abstract

In this paper, we study a one-dimensional dissipative system of piezoelectric beams with magnetic effect, based on the work of Morris and Özer (in: The proceedings of 52nd IEEE conference on decision & control, pp 3014–3019, 2013). Our main goal is to prove the system’s exponential stability independent of any relation between the coefficients using terms of feedback at the boundary and consequently prove their equivalence with the exact observability at the boundary.

Keywords

Piezoelectric beams Exponential decay Boundary observability 

Mathematics Subject Classification

Primary 99Z99 Secondary 00A00 

Notes

Acknowledgements

The authors are grateful to the anonymous referees for their constructive remarks, which have enhanced the presentation of this paper.

Funding

A.J.A. Ramos and S.S. Jesus thank PIBIC-INTERIOR/UFPA for financial support. D.S. Almeida Júnior thanks the CNPq for financial support through the projects “Control and stabilization of Timoshenko systems: mathematical aspects, theoretical numerics and computational” (CNPq Grant 458866/2014-8, Universal Project - 2014) and “New guidelines for dissipative Timoshenko type systems at light of the second spectrum” (CNPq Grant 310423/2016-3).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • A. J. A. Ramos
    • 1
    • 2
    Email author
  • M. M. Freitas
    • 1
    • 2
  • D. S. AlmeidaJr.
    • 1
  • S. S. Jesus
    • 2
  • T. R. S. Moura
    • 2
  1. 1.PhD Program in MathematicsFederal University of ParáBelémBrazil
  2. 2.Faculty of MathematicsFederal University of ParáSalinópolisBrazil

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