Input-to-state stability of impulsive switched hybrid time-delay systems with delayed impulse effects

This paper investigates the problem of input-to-state stability (ISS) of impulsive switched hybrid time-delay systems with delayed impulse effects. By employing the method of multiple Lyapunov-Krasovskii (L-K) functionals, two novel ISS criteria are established. It is shown that, when all the subsystems governing the continuous dynamics of system (1) are stable but the impulse are destabilizing, the ISS property of system can be preserved, if the delayed impulses satisfy a dwell-time condition. On the other hand, the opposite aspect is also given. An illustrative example shows that the proposed results are effective and can generalize the existing results.