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In this paper, we analyze a systematically designed and easily tunablebackstepping-based boundary control concept developed by Thull, Wild, and Kugi(2006) for a gantry crane with heavy chain and payload. The correspondingclosed-loop system is formulated as an abstract evolution equation in anappropriate Hilbert space. Non-restrictive conditions for the controllercoefficients are derived, under which the solutions are described by a$C_0$-semigroup of contractions, and are asymptotically stable. Moreover, byapplying Huang's theorem we can finally even show that under these conditionsthe controller renders the closed-loop system exponentially stable.

Closed-loop Stability Analysis of a Gantry Crane with Heavy Chain