Exponential stabilization of an axially moving string by linear boundary feedback

The system modeled by an axially moving string and a mass-damper-spring (MD S) controller applied at the right-hand side (RHS) boundary of the string i s considered. The feature of the controller is not restricted at all, and i s determined by the system implicitly. The mathematical model of this syste m is composed of an ordinary differential equation (ODE) describing the MDS and a partial differential equation (PDE) describing the string. The C-0 s emigroup theory provides an elegant state space representation for the anal ysis of the coupled system. The exponential stability is verified through t he total mechanical energy dissipation and the semigroup theory. The lower bound of the feedback gain is obtained. (C) 1999 Elsevier Science Ltd. All rights reserved.