We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as zero-input global uniform asymptotic stability (0-GUAS), are covered by employing a two-measure framework and considering stability of both weak (decay depends only on elapsed time) and strong (decay depends on elapsed time and the number of impulses) flavors. By contrast to many existing results, the stability state bounds imposed are uniform with respect to initial time and also with respect to classes of impulse-time sequences where the impulse frequency is eventually uniformly bounded. We show that the considered classes of impulse-time sequences are substantially broader than other previously considered classes, such as those having fixed or (reverse) average dwell times, or impulse frequency achieving uniform convergence to a limit (superior or inferior). Moreover, our sufficient conditions are not more restrictive than existing ones when particularized to some of the cases covered in the literature, and hence in these cases our results allow to strengthen the existing conclusions.

中文翻译：

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具有最终均匀有界脉冲频率的非线性时变脉冲系统的均匀稳定性

我们为非线性和时变脉冲系统的稳定性提供了新的充分条件。这些条件概括、扩展和加强了许多现有结果。不同类型的输入到状态稳定性 (ISS) 以及零输入全局均匀渐近稳定性 (0-GUAS)，通过采用双测度框架并考虑两个弱（衰减仅取决于经过时间）和强烈（衰减取决于经过的时间和脉冲数）味道。与许多现有结果相比，施加的稳定状态边界对于初始时间以及脉冲频率最终统一有界的脉冲时间序列类别是一致的。我们表明，所考虑的脉冲时间序列类别比以前考虑的其他类别要广泛得多，例如具有固定或（反向）平均驻留时间的类别，或实现统一收敛到极限（上或下）的脉冲频率。此外，当特定于文献中涵盖的某些案例时，我们的充分条件并不比现有条件更具限制性，因此在这些案例中，我们的结果可以加强现有结论。