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Exponential Stabilization of a Flexible Structure: A Delayed Boundary Force Control Versus a Delayed Boundary Moment Control

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Abstract

The main concern of this paper is to study the boundary stabilization problem of the disk-beam system. To do so, we assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. First, we show that in both cases, the system is well-posed in an appropriate functional space. Next, the exponential stability property is established. Finally, the obtained outcomes are ascertained through numerical simulations.

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Data Availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to thank the associate editor and the six referees for the careful reading of this paper and for their valuable suggestions and comments that have led to an improved version of this article.

Funding

This work was supported and funded by Kuwait University, Research Project No. (SM03/21).

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Kuwait University, 13060, Safat, Kuwait

    Boumediène Chentouf & Nejib Smaoui

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  1. Boumediène Chentouf
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  2. Nejib Smaoui
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Contributions

B.C. wrote sections 1, 2 and 3. N.S. wrote sections 1 and 4, and prepared Figures 2-15. The two authors reviewed the manuscript.

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Correspondence to Nejib Smaoui.

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Chentouf, B., Smaoui, N. Exponential Stabilization of a Flexible Structure: A Delayed Boundary Force Control Versus a Delayed Boundary Moment Control. Qual. Theory Dyn. Syst. 23, 112 (2024). https://doi.org/10.1007/s12346-024-00969-2

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