The input-to-state stability (ISS) and integral input-to-state stability (iISS) problems are addressed for a family of impulsive switched hybrid time-delay systems with delayed impulses. Employing the multiple Lyapunov–Krasovskii functionals method, sufficient conditions are established guaranteeing the ISS/iISS property of the given system. Here, the discrete dynamics are destabilizing (stabilizing) while the continuous dynamics may be stable (unstable). The impulsive, switching signals and delayed impulses are all considered which satisfy some dwell-time conditions. Two illustrative examples are presented to show that the proposed results are effective and a practical example is given to show a background of our model.
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