The effects of delays on rank-one stabilizing controls in vibrating systems

Results are presented on the effect of small time delays which occur in the feedback of a class of infinite-dimensional vibrating systems whose uncontrolled versions are either conservative or uniformly damped. It is shown that conservative systems which are exponentially damped by feedback can be transformed into unstable systems if arbitrarily small time delays are introduced into the feedback. In the case of uniformly damped systems it can sometimes happen that a feedback which enhances stability can induce periodic or even exponentially unbounded solutions if arbitrarily small time delays are introduced into it