BOUNDARY STABILIZATION of A FLEXIBLE STRUCTURE with DYNAMIC BOUNDARY CONDITIONS VIA ONE TIME-DEPENDENT DELAYED BOUNDARY CONTROL

Boumediène Chentouf*, Sabeur Mansouri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This article deals with the dynamic stability of a flexible cable attached at its top end to a cart and a load mass at its bottom end. The model is governed by a system of one partial differential equation coupled with two ordinary differential equations. Assuming that a time-dependent delay occurs in one boundary, the main concern of this paper is to stabilize the dynamics of the cable as well as the dynamical terms related to the cart and the load mass. To do so, we first prove that the problem is well-posed in the sense of semigroups theory provided that some conditions on the delay are satisfied. Thereafter, an appropriate Lyapunov function is put forward, which leads to the exponential decay of the energy as well as an estimate of the decay rate.

Original languageEnglish
Pages (from-to)1127-1141
Number of pages15
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume15
Issue number5
DOIs
Publication statusPublished - May 2022
Externally publishedYes

Keywords

  • boundary time-dependent delay
  • exponential stability
  • Lyapunov function
  • moment control
  • Overhead crane

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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