Input-to-state stability for impulsive switched systems with incommensurate impulsive switching signals

•Input-to-state stability (ISS) property of impulsive switched systems with inconsistent impulsive switching signals is firstly studied.•With the help of Lyapunov method and average dwell-time (ADT) approach, some sufficient conditions are provided to cope with the problem of ISS for impulsive switched systems, where the hybrid effects of stabilizing impulses and destabilizing impulses are taken into account.•When some of modes are not ISS, a relationship such that the impulsive switched systems are ISS can be established among ADT scheme, impulses, and the total dwell-time between ISS and non-ISS modes.