Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework we describe some new global controllability tests for hybrid control systems exploiting the geometry and the topology of the set of jump points, where the instantaneous change of dynamics take place. Controllability is understood as the existence of a feasible trajectory for the system joining any two given points. As a result we describe examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.

中文翻译：

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几何混合控制系统的全局可控性测试

混合系统的特点是具有连续动态和离散事件之间的相互作用。本文的贡献是为混合系统提供一种新颖的几何公式​​，以便可以添加控件。使用这个框架，我们描述了混合控制系统的一些新的全局可控性测试，这些测试利用了一组跳跃点的几何形状和拓扑结构，其中发生了动态的瞬时变化。可控性被理解为系统连接任意两个给定点的可行轨迹的存在。因此，我们描述的例子中没有一个连续控制系统是可控的，但由于跳跃集的特性，相关的混合系统是可控的。