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

Abstract

This work mainly studies the input-to-state stability (ISS) property of impulsive switched systems with incommensurate impulsive switching signals, where the switching instant is different from the impulse jump instant. 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 system, where the hybrid effects of stabilizing impulses and destabilizing impulses are taken into account. It is shown that when all of the modes are ISS, a switched system under an ADT scheme is ISS even if there exist hybrid impulses. Moreover, when none of the modes is ISS, we show that ISS still can be achieved under the designed ADT scheme couples with hybrid impulses. Furthermore, when some of modes are not ISS, a relationship such that impulsive switched system is ISS can be established among ADT scheme, impulses, and total dwell-time between ISS and non-ISS modes. Two illustrative examples are presented, with their numerical simulations, to demonstrate the effectiveness of main results.