Averaging of hybrid dynamical systems with disturbances

We present an averaging approach for investigation of input-to-state stability (ISS) for a class of hybrid systems. Two recently proposed definitions of averages (strong and weak averages) for time varying systems with disturbances are adapted to a class of hybrid systems. Assuming that the average systems is forward complete, we show an appropriate closeness of solutions on compact time intervals between the actual system and its strong or week average. We also show that ISS of the weak or strong average implies respectively semi-global practical derivative ISS (SP-DISS) or semi-global practical ISS (SP-ISS).