Stabilization of structurally damped systems by pointwise time-delayed feedback control

A class of multi-dimensional damped distributed parameter systems with pointwise time-delayed displacement is considered. The linear systems with delayed control action are transformed into equivalent systems without delays. It is shown that the feedback gain control exists and asymptotically stabilizes the closed-loop modal system. An analysis of the effectiveness of using pointwise time-delayed displacement under these condition is studied. Specific numerical results are given for a structurally damped beam for various parameters when the pointwise delayed displacement feedback control is applied.