论文标题
路径完整技术和基于内存的Lyapunov功能的解释性
Interpretability of Path-Complete Techniques and Memory-based Lyapunov functions
论文作者
论文摘要
我们研究了路径完整的Lyapunov函数，这是由组件（即自动机）和功能分量（一组候选Lyapunov函数，称为模板）描述的开关系统的稳定性标准。我们根据所谓的基于内存的Lyapunov函数介绍了一类标准，这些功能在文献中概括了几种技术。我们的主要结果是等效结果：任何路径完整的Lyapunov函数等于基于内存的Lyapunov函数，但是在另一个模板上定义。通过学术示例，我们在数值效率方面显示了结果的有用性。
We study path-complete Lyapunov functions, which are stability criteria for switched systems, described by a combinatorial component (namely, an automaton), and a functional component (a set of candidate Lyapunov functions, called the template). We introduce a class of criteria based on what we call memory-based Lyapunov functions, which generalize several techniques in the literature. Our main result is an equivalence result: any path-complete Lyapunov function is equivalent to a memory-based Lyapunov function, however defined on another template. We show the usefulness of our result in terms of numerical efficiency via an academic example.
