This paper considers the problem of practical finite-time stability (PFTS) for switched nonlinear time-varying (SNTV) systems. Starting with nonlinear time-varying (NTV) systems, a new sufficient condition is proposed to verify the PFTS of systems by using an improved Lyapunov function. Then, the results obtained are extended to study the PFTS of SNTV systems. Two stability conditions are proposed for SNTV systems under arbitrary switching, moreover, the time and region of convergence are also given. Furthermore, an initial state-dependent dwell time method is introduced to study the PFTS of SNTV systems. Three stability conditions are proposed by using the methods of initial state-dependent minimum dwell time (ISD-MDT) and initial state-dependent average dwell time (ISD-ADT), respectively. The comparisons between the obtained results and the existing results are also given, and the obtained results are extended to impulsive switched nonlinear time-varying (ISNTV) systems. Finally, a numerical example is provided to illustrate the theoretical results.

本文考虑了切换非线性时变（SNTV）系统的实际有限时间稳定性（PFTS）问题。从非线性时变（NTV）系统开始，提出了一个新的充分条件，以通过使用改进的Lyapunov函数来验证系统的PFTS。然后，将获得的结果扩展到研究SNTV系统的PFTS。提出了SNTV系统在任意切换条件下的两个稳定性条件，并给出了收敛时间和收敛区域。此外，引入了一种与状态有关的初始停留时间方法来研究SNTV系统的PFTS。分别使用初始状态相关的最小驻留时间（ISD-MDT）和初始状态相关的平均驻留时间（ISD-ADT）的方法，提出了三种稳定性条件。还给出了所得结果与现有结果之间的比较，并将所得结果扩展到脉冲开关非线性时变（ISNTV）系统。最后，提供了一个数值例子来说明理论结果。