Input-to-state stability and integral input-to-state stability for impulsive switched systems with time-delay under asynchronous switching

This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of impulsive switched systems with time-delay under asynchronous switching, using the method of multiple Lyapunov-Krasovskii functionals. The asynchronous switching means that the switchings between the candidate controllers and system modes are not synchronous due to the switching delay. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in the ISS/iISS sense with the matched controller if the length of the impulsive interval is large enough. Conversely, when the delayed continuous dynamics are ISS/iISS but the discrete dynamics governing the impulses are not, the ISS/iISS property of the hybrid system can be retained with the matched controller if the impulsive interval and the switching delay are small enough. Finally, two illustrative examples are presented to demonstrate the effectiveness of the results.