  It is shown that impulsive systems of nonlinear, time-varying and/or switched
form that allow a stable global state weak linearization are jointly
input-to-state stable (ISS) under small inputs and integral ISS (iISS). The
system is said to allow a global state weak linearization if its flow and jump
equations can be written as a (time-varying, switched) linear part plus a
(nonlinear) pertubation satisfying a bound of affine form on the state. This
bound reduces to a linear form under zero input but does not force the system
to be linear under zero input. The given results generalize and extend
previously existing ones in many directions: (a) no (dwell-time or other)
constraints are placed on the impulse-time sequence, (b) the system need not be
linear under zero input, (c) existence of a (common) Lyapunov function is not
required, (d) the perturbation bound need not be linear on the input.
