Stabilization of a Hybrid System: An Overhead Crane with Beam Model

Eduard Feireisl and Geoffrey O'Dowd

Abstract: The object of this paper is the study of a model of an overhead crane consisting of a beam carrying a load, fixed to a moving platform. Stabilization of the system is achieved by means of a monotone feedback law taking into account the position and the velocity of the platform. We then prove that strong stabilization occurs without global monotonicity, thanks to an energy estimate for solutions of a variational nonlinear nonautonomous evolution equation.

Keywords: Hybrid systems; beam equation; stabilization by feedback law; $\omega$-limit sets.

Classification (MSC2000): 93D15; 47H20.

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