Input-to-state stability of impulsive switched nonlinear time-delay systems with two asynchronous switching phenomena

This summary addresses the input-to-state stability (ISS) and integral ISS (iISS) problems of impulsive switched nonlinear time-delay systems (ISNTDSs) under two asynchronous switching effects. In our investigated systems, impulsive instants and switching instants do not necessarily coincide with each other. Meanwhile, systems switching signals are not simultaneous with the corresponding controllers switching signals, which will induce instability seriously, and cause many difficulties and challenges. By utilizing methods of Lyapunov-Krasovskii and Lyapunov-Razumikhin, mode-dependent average dwell time approach, and mode-dependent average impulsive interval technique, some stability criteria are presented for ISNTDSs under two asynchronous switching effects. Our proposed results improve the related existing results on the same topic by removing some restrictive conditions and cover some existing results as special cases. Finally, some simulation examples are presented to illustrate the effectiveness and advantages of our results.