In this article, we elaborated on the problem of fixed time stability (FxTS) of nonlinear impulsive systems. For handing this problem, we propose a new concept of fixed-time stable function set (FTSFS). By taking advantage of definitions of FTSFS and average impulsive interval, a unified FxTS criterion of nonlinear impulsive systems is presented, which is applicable to both destabilising impulses and stabilising impulses. Comparing with the available work, the proposed Lyapunov function is allowed to possess indefinite derivatives when deriving from the state trajectory of nonlinear impulsive systems. Finally, two numerical examples are provided to support the proposed criterion.

在本文中，我们详细阐述了非线性脉冲系统的固定时间稳定性（FxTS）问题。为了解决这个问题，我们提出了固定时间稳定函数集（FTSFS）的新概念。利用FTSFS和平均脉冲区间的定义，提出了一个统一的非线性脉冲系统FxTS判据，该判据既适用于失稳脉冲，也适用于稳定脉冲。与现有工作相比，所提出的李雅普诺夫函数在从非线性脉冲系统的状态轨迹导出时允许具有不定导数。最后，提供了两个数值例子来支持所提出的标准。