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Abstract
In this paper, we continue the earlier work [Lu, L., & Wang, D. L. (2017). Dynamic boundary feedback of a pendulum coupled with a viscous damped wave equation. In Proceedings of the 36th Chinese Control Conference(CCC) (pp. 1676–1680)] on study the stability of a pendulum coupled with a viscous damped wave equation model. This time we get the exponential stability result which is much better than the previous strong stability. By a detailed spectral analysis and operator separation, we establish the Riesz basis property as well as the spectrum determined growth condition for the system. Finally, the exponential stability of the system is achieved.
Acknowledgements
We thank Editor-in-Chief, Associate editor, and Reviewers for their efforts on the paper.
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No potential conflict of interest was reported by the authors.
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Notes on contributors
Lu Lu
Lu Lu received her B.S. degree in Mathematics and Applied Mathematics from Anhui Normal University in 2008, and Ph.D degree in Applied Mathematics from Beijing Institute of Technology in 2016. Her research interests focus on the control theory of distributed parameter systems.
Bao-Qing Lu
Bao-Qing Lu received his B.S. degree in Chemistry from Shandong University in 2011 and M.S. diploma from School of Statistics of Renmin University of China in 2018. His research interests focus on the Applications of Statistics.