  We consider a two-player linear-state differential game, where one player
intervenes continuously in the game, while the other implements an impulse
control. When the impulse instants are exogenous, we obtain the classical
result in linear-state differential games that open-loop and feedback Nash
equilibria coincide. When the impulse instants are endogenous, we show that
this result no longer holds. In particular, the two equilibria are different.
We show that the impulse level is a constant in both equilibria. More
importantly, in the open-loop case, we show that the equilibrium number of
impulses is at most one, while there can be at most two impulses in the
feedback case.
