This article studies the problem of finite-time stability (FTS) and finite-time contractive stability (FTCS) for nonlinear impulsive systems, where the possibility of time delay in impulses is fully considered. Some sufficient conditions for FTS/FTCS are constructed in the framework of Lyapunov function methods. A relationship between impulsive frequency and the time delay existing in impulses is established to reveal FTS/FTCS performance. As an application, we apply the theoretical results to finite-time state estimation of neural networks, including time-varying neural networks and switched neural networks. Finally, two illustrated examples are given to show the effectiveness and distinctiveness of the proposed delay-dependent impulsive schemes.

中文翻译：

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非线性脉冲系统的有限时间稳定性及其在神经网络中的应用


本文研究了非线性脉冲系统的有限时间稳定性（FTS）和有限时间收缩稳定性（FTCS）问题，其中充分考虑了脉冲时滞的可能性。在李亚普诺夫函数方法的框架内构造了FTS/FTCS的一些充分条件。建立脉冲频率与脉冲中存在的时间延迟之间的关系以揭示 FTS/FTCS 性能。作为应用，我们将理论结果应用于神经网络的有限时间状态估计，包括时变神经网络和切换神经网络。最后，给出了两个示例来说明所提出的时滞相关脉冲方案的有效性和独特性。