In this paper, we study the stabilization problem of a flexible cable with two rigid loads which is described by two kinds of hyperbolic equations. From the engineering point of view, the model can be regarded as a distributed parameter overhead crane which conveys two loads simultaneously. After deriving a control law which does not increase an energy defined for the model, we prove the asymptotic stability of the closed-loop system, using the LaSalle's invariance principle. Finally, we show that the control law works effectively through a numerical simulation.
"Stabilization of a Flexible Cable with Two Rigid Loads." Japan J. Indust. Appl. Math. 23 (3) 225 - 237, October 2006.