Exponential stabilization of a flexible structure with a local interior control and under the presence of a boundary infinite memory

Boumediène Chentouf*, Sabeur Mansouri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we deal with the interior stabilization problem of a flexible structure governed by a hyperbolic partial differential equation coupled to two ordinary differential equations. Contrary to the previous works on the system, the boundary control is subject to the presence of an infinite memory term. In order to deal with such a nonlocal term, the minimal state approach is invoked. Specifically, a localized interior control is proposed in order to compensate the infinite memory effect. Thereafter, reasonable assumptions on the memory kernel are evoked so that the closed-loop system is shown to be well-posed thanks to semigroups theory of linear operators. Furthermore, the resolvent method is used to establish the exponential stability of the system.

Original languageEnglish
JournalMathematical Methods in the Applied Sciences
DOIs
Publication statusAccepted/In press - 2022
Externally publishedYes

Keywords

  • exponential stability
  • flexible structure
  • infinite memory
  • local interior control
  • minimal state

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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