A linear time invariant system with uncertain initial conditions, perturbed parameters, and active disturbance signals operates in open loop as a result of feedback failure or interruption. The objective is to find an optimal input signal that drives the system for the longest time without exceeding specified error bounds, to allow maximal time for feedback reactivation. It is shown that such a signal exists, and that it can be replaced by a bang-bang signal without significantly affecting performance. The use of bang-bang signals simplifies calculation and implementation.