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D. Stürzer, A. Arnold, A. Kugi:
"Closed-loop stability analysis of a gantry crane with heavy chain";
in: "ASC Report 16/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 17.

In this paper, we systematically analyze the backstepping based bound-ary control concept developed in [22] for a gantry crane with heavy chain and payload. The corresponding closed-loop system is formulated as an abstract evolution equa-tion in an appropriate Hilbert space. Conditions for the coefficients of the boundary control are derived, under which the solutions are described by a C0-semigroup of contractions, and are asymptotically stable. By applying Huang´s theorem we can finally even show that under these conditions the controller renders the closed-loop system exponentially stable.

http://www.asc.tuwien.ac.at/preprint/2016/asc16x2016.pdf