Allocation of poles of delayed systems related to those associated with their undelayed counterparts

The existence of closed bounded balls in the complex plane the union of which contains all the poles of a system subject to delayed dynamics with constant internal point delays is proved. Each ball is centred at each pole of the associated delay-free system and it may contain either a finite or infinite number of poles of the delayed system. As a result, the stability of the delay free system is preserved with a sufficiently small contribution from delayed dynamics