Even some internally damped vibrating control systems lose stability when small delays occur in their feedbacks

Results are presented concerning the effects of small time delays in the controls of a class of infinite-dimensional linear vibrating systems whose homogeneous versions (i.e. those for which the controls are zero) are uniformly asymptotically stable. It is shown that an undelayed feedback control involving the velocity vector does not destroy and may even enhance stability. However, in some instances arbitrarily small time delays in the feedback result in periodic and even unstable motions. It is shown that this destabilization phenomenon can be avoided if the feedback gain is chosen to be sufficiently small