The effects of time delays on collocated as well as non-collocated point control of classically damped discrete dynamic systems have been examined. Controllers of PID type have been considered. Analytical estimates of time delays to maintain/obtain stability for small gains have been given. Several new results dealing with the effect of time delays on collocated and non-collocated control designs are obtained. It is shown that undamped structural systems cannot be stabilized with pure velocity (or integral) feedback without time delays while using a controller that is not collocated with the sensor, when the mass matrix is diagonal. However, with the appropriate choice of time delays, for certain classes of commonly occurring structural systems, stable noncollocated control can be achieved. Analytical results providing the upper bound on the controller’s gain necessary for stability have been presented. The theoretical results obtained are illustrated and verified with numerical examples.