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It is well known that the performance of computer controlled systems is heavily affected by delays and jitter occurring in the control loops, which are mainly caused by the interference introduced by other concurrent activities. A common approach adopted to reduce delay and jitter in periodic task systems is to decrease relative deadlines as much as possible, but without jeopardising the schedulability of the task set. In this paper, we formally characterise the region of admissible deadlines so that the system designer can appropriately select the desired values to maximise a given performance index defined over the task set. Finally we also provide a sufficient region of feasible deadlines which is proved to be convex.