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In this paper, we continue the earlier work [Lu, L., &amp; 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.

Exponential stability of a pendulum in dynamic boundary feedback with a viscous damped wave equation