  For time-invariant (nonimpulsive) systems, it is already well-known that the
input-to-state stability (ISS) property is strictly stronger than integral
input-to-state stability (iISS). Very recently, we have shown that under
suitable uniform boundedness and continuity assumptions on the function
defining system dynamics, ISS implies iISS also for time-varying systems. In
this paper, we show that this implication remains true for impulsive systems,
provided that asymptotic stability is understood in a sense stronger than usual
for impulsive systems.
