In this article, we study the finite-time stability (FTS) and finite time stabilization problems for a class of switched impulsive systems evolving on an arbitrary time domain. This problem is formulated using time scale theory where the time domain can be continuous, discrete, union of disjoint intervals with variable gaps and variable lengths or any combination of these. Using common Lyapunov-quadratic and Lyapunov-like functions, we establish sufficient conditions to ensure the FTS results. Further, to solve the stabilization problem, we design state feedback controllers. We have illustrated the effectiveness of the obtained analytical results though numerical examples.

在本文中，我们研究了一类在任意时域上发展的切换脉冲系统的有限时间稳定性（FTS）和有限时间稳定问题。这个问题是使用时标理论来提出的，其中时域可以是连续的，离散的，不相交间隔的并集以及可变的间隙和可变的长度，或者是这些的任意组合。使用常见的Lyapunov二次函数和类Lyapunov函数，我们建立了充分条件来确保FTS结果。此外，为了解决稳定性问题，我们设计了状态反馈控制器。我们通过数值例子说明了所获得的分析结果的有效性。