  For general time-varying or switched (nonlinear) systems, converse Lyapunov
theorems for stability are not available. In these cases, the integral
input-to-state stability (iISS) property is not equivalent to the existence of
an iISS-Lyapunov function but can still be characterized as the combination of
global uniform asymptotic stability under zero input (0-GUAS) and uniformly
bounded energy input-bounded state (UBEBS). For impulsive systems, asymptotic
stability can be weak (when the asymptotic decay depends only on elapsed time)
or strong (when such a decay depends also on the number of impulses that
occurred). This paper shows that the mentioned characterization of iISS remains
valid for time-varying impulsive systems, provided that stability is understood
in the strong sense.
