  Most of the existing characterizations of the integral input-to-state
stability (iISS) property are not valid for time-varying or switched systems in
cases where converse Lyapunov theorems for stability are not available. This
note provides a characterization that is valid for switched and time-varying
systems, and shows that natural extensions of some of the existing
characterizations result in only sufficient but not necessary conditions. The
results provided also pinpoint suitable iISS gains and relate these to supply
functions and bounds on the function defining the system dynamics.
