  We consider nonlinear impulsive systems on Banach spaces subjected to
disturbances and look for dwell-time conditions guaranteeing the the ISS
property. In contrary to many existing results our conditions cover the case
where both continuous and discrete dynamics can be unstable simultaneously.
Lyapunov type methods are use for this purpose. The effectiveness of our
approach is illustrated on a rather nontrivial example, which is feedback
connection of an ODE and a PDE systems.
