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.

中文翻译：

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Lyapunov函数的分段结构和混合系统的严格检验的减少条件

我们提出一类具有分段结构的局部Lipschitz函数，以用作混合动力系统的Lyapunov函数。服从动力学的某些规律性，我们表明Lyapunov不等式只能在稠密集合上进行检查，因此我们避免在Lyapunov函数的不可微点上对其进行检查。还讨论了与其他类别的本地Lipschitz或分段正则函数的连接，并包括了对混合动力系统的应用。