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.

中文翻译：

---

具有两种异步切换现象的脉冲切换非线性时滞系统的输入状态稳定性

本摘要解决了在两种异步切换效应下的脉冲切换非线性时滞系统（ISNTDS）的输入状态稳定性（ISS）和积分ISS（iISS）问题。在我们研究的系统中，脉冲瞬间和切换瞬间不一定彼此一致。同时，系统切换信号不能与相应的控制器切换信号同时进行，这将导致严重的不稳定，并带来许多困难和挑战。利用Lyapunov-Krasovskii和Lyapunov-Razumikhin的方法，模式相关的平均停留时间方法和模式相关的平均脉冲间隔技术，提出了两种异步切换效应下ISNTDS的稳定性准则。我们提出的结果通过消除一些限制条件来改善同一主题上相关的现有结果，并以特殊情况覆盖了一些现有结果。最后，给出了一些仿真示例，以说明我们的结果的有效性和优势。