The optimal impulsive control problem for a system with a single discrete delay is studied. In such systems the control consists only of a sequence of modulated impulses, the control variables being the impulse times and their magnitudes. It is assumed that the systems considered all have a refractory period, in the sense that once an action is taken, it takes a non-infinitesimal amount of time before a subsequent action can be taken. Necessary conditions for a stationary solution are derived and shown to extend those of the delay free case.
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