Dwell-time stability conditions for infinite dimensional impulsive systems

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