论文标题
为冲动系统的时变ISS与Lyapunov功能的构建
Construction of time-varying ISS-Lyapunov Functions for Impulsive Systems
论文作者
论文摘要
时间变化的ISS与冲动系统的ISS-Lyapunov功能为ISS提供了必要和充分的条件。与经典的ISS-Lyapunov功能相比，该属性使它们成为稳定性分析的功能更强大的工具，仅提供足够的ISS条件。此外，随时间变化的ISS与Lyapunov函数涵盖了具有连续和离散动态的同时不稳定性的系统，候选人ISS-Lyapunov函数仍然尚无定论。本文通过提出了一种从候选ISS-Lyapunov函数构建时变的ISS与Lyapunov功能的方法来链接这两个概念，从而有效地结合了候选ISS-Lyapunov函数的易于构建，并与保证的时变ISS-Lyapunov功能相结合。
Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.
