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Equivalence between exponential stabilization and observability inequality for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights

  • * Corresponding authors: wjliu@nuist.edu.cn (W. Liu), jeremias@ufpa.br (M. Santos)

    * Corresponding authors: wjliu@nuist.edu.cn (W. Liu), jeremias@ufpa.br (M. Santos) 

† These authors contributed equally to this work

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  • This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller with a time-varying delay. Under appropriate assumptions on the time-varying delay term and time-dependent weights, we obtain exponential stability estimates by using the multiplicative technique, and prove the equivalence between stabilization and observability.

    Mathematics Subject Classification: Primary: 35L05, 35L15; Secondary: 93D15.


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