发表机构
University of California Santa Cruz（加州大学圣克鲁兹分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出几何混合动力系统在流形上的建模框架，利用非光滑分析推导稳定性条件，并建立几何与度量稳定性等价性，引入混合Lyapunov定理和不变性原理。
AI 中文摘要
我们提出了一个框架，用于将几何混合动力系统建模和分析为$C^1$-流形上的混合包含。利用流形上的非光滑和集值分析工具，我们推导了此类系统存在非平凡解的坐标无关充分条件。我们提出了紧集的均匀稳定性和吸引性的几何概念，并建立了当流形赋予黎曼结构时，这些概念与基于度量的稳定性概念的等价性。我们还引入了非光滑Lyapunov函数和一个混合Lyapunov定理，为紧集的均匀全局渐近稳定性提供充分条件。最后，通过刻画预紧解的$\omega$-极限集，我们推导了几何混合动力系统的混合不变性原理。结果通过几个运行示例进行了演示。
英文摘要
We present a framework for the modeling and analysis of geometric hybrid dynamical systems as hybrid inclusions on $C^1$-manifolds. Using tools from nonsmooth and set-valued analysis on manifolds, we derive coordinate-independent sufficient conditions for the existence of nontrivial solutions to this type of systems. We present geometric notions of uniform stability and attractivity of compact sets, and establish their equivalence to metric-based stability notions when the manifold is endowed with a Riemannian structure. We also introduce nonsmooth Lyapunov functions and a hybrid Lyapunov theorem providing sufficient conditions for uniform global asymptotic stability of compact sets. Finally, by characterizing $ω$-limit sets of precompact solutions, we derive a hybrid invariance principle for geometric hybrid dynamical systems. The results are demonstrated through several running examples.
Comments28 pages, 4 figures. Under review at IEEE Transactions on Automatic Control
