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

(Integral-)ISS of switched and time-varying impulsive systems based on global state weak linearization