The system modeled by an axially moving string and a mass-damper-spring (MDS) controller applied at the right-hand side (RHS) boundary of the string is considered. The feature of the controller is not restricted at all, and is determined by the system implicitly. The mathematical model of this system is composed of an ordinary differential equation (ODE) describing the MDS and a partial differential equation (PDE) describing the string. The C-0 semigroup theory provides an elegant state space representation for the analysis of the coupled system. The exponential stability is verified through the total mechanical energy dissipation and the semigroup theory. The lower bound of the feedback gain is obtained.