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M. Miletic, D. Stürzer, A. Arnold, A. Kugi:
"Stability of an Euler-Bernouilli beam with a nonlinear dynamic feedback system";
in: "ASC Report 19/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 21.

This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises
nonlinear dynamic boundary controllers satisfying the nonlinear KYP lemma as well as the interaction with a nonlinear passive environment. Global-in-time wellposedness and asymptotic stability
is rigorously proven for the resulting closed-loop PDE-ODE system. The analysis is based on semigroup theory for the corresponding first order evolution problem. For the large-time analysis,
precompactness of the trajectories is shown by deriving uniform-in-time bounds on the solution and its time derivatives.

http://www.asc.tuwien.ac.at/preprint/2015/asc19x2015.pdf