Stabilization of elastic systems using sampled data feedback

There is substantial interest in use of feedback control techniques to achieve active stabilization of elastic systems. Most previous research has focused on use of analog feedback techniques for achieving such stabilization. Use of sampled data output feed-back to achieve stabilization of an elastic system is examined in this work. The basic formulations are stated in terms of second order vector recursions. The suggested controller form consists of an output estimator and estimated output feedback. Sufficient conditions for closed loop stability are developed. A detailed development is given for the special case of an undamped finite dimensional elastic system. Two cases where the feedback depends only on velocity measurement data and only on displacement measurement data are considered. In each case explicit conditions on the gains are given for which the closed loop is guaranteed to be stable.