论文标题
Lyapunov功能的分段结构和密集检查的降低了混合系统的条件
Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems
论文作者
论文摘要
我们提出了一类具有分段结构的本地Lipschitz函数，以用作混合动力学系统的Lyapunov函数。在某种规律性的情况下，我们表明只能在密集的集合上检查Lyapunov的不平等现象，因此我们避免在Lyapunov函数的非分辨率点检查它们。还讨论了与其他类别的Lipschitz或分段常规功能的连接，并包括对混合动力学系统的应用。
We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise regular functions are also discussed and applications to hybrid dynamical systems are included.
