On the stabilization of a cable with a tip mass

Abstract

In this note, we consider a vertical cable which is pinched at the upper end. A mass is attached at the lower end where a control force is also applied. We show that this hybrid system is uniformly stabilized by choosing a suitable control law for the control force depending on the velocity and angular velocity at the free end. Moreover for specific values of the feedback coefficients, we obtain the rate of decay of the energy of the system.