Input/output-to-state stability of impulsive switched systems

This paper studies the input/output-to-state stability (IOSS) of impulsive switched systems. With the help of Lyapunov and average dwell-time (ADT) methods, some sufficient conditions for IOSS of impulsive switched systems are obtained, where both types of impulses, stabilizing impulses and destabilizing impulses, are considered. It is shown that when all of the modes are IOSS, a switched system under an ADT scheme is IOSS even if there exist destabilizing impulses, and when none of the modes is IOSS, IOSS can still be achieved under the designed ADT scheme coupled with stabilizing impulses. In particular, for a special case in which an impulsive switched system is composed of some IOSS modes and some non-IOSS modes, a relationship is established among the ADT scheme, impulses, and the total dwell time between non-IOSS and IOSS modes such that the impulsive switched system is IOSS. Two examples are provided to illustrate the applications of our results.