For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stability (ISS) property is strictly stronger than integral input-to-state stability (iISS). Very recently, we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics, ISS implies iISS also for time-varying systems. In this paper, we show that this implication remains true for impulsive systems, provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems.

中文翻译：

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强大的ISS意味着时变脉冲系统具有强大的iISS

对于时不变（非脉冲）系统，众所周知，输入状态稳定性（ISS）特性比积分输入状态稳定性（iISS）严格更强。最近，我们已经表明，在对定义系统动力学的函数进行适当的有界和连续性假设的前提下，ISS意味着iISS也适用于时变系统。在本文中，我们表明，对于脉冲系统来说，这种含义仍然成立，前提是从某种意义上说，对于脉冲系统，渐近稳定性的理解要强于通常的情况。