We revisit two examples of elastic control systems which are stabilized by boundary feedback and then destabilized when time delays occur in the feedback. In the first example, a wave equation with a feedback gain greater than or equal to one, arbitrary divergence rates are obtained for small time delays. In the second example, a Euler-Bernoulli beam, any time delay results in an arbitrary divergence rate.
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Richard Datko (1997) studied this question.