A study of moving string with partial state feedback

In this paper, we present the optimal gain for the boundary control of moving string system with which the transverse vibration decays with the largest negative exponent to zero exponentially. Also we use semi-difference scheme to convert the system to a lumped system and prove that the latter system is exponentially stable. For the case that moving string system does not have boundary control, we prove that every solution of the system is bounded and the total mechanical energy is changing periodically.