关于平面系统中重置诱导周期轨迹的全局结果
Global results on reset-induced periodic trajectories of planar systems
AI总结：
本文研究了由重置反馈诱导的渐近稳定的周期轨迹的存在性，通过平面系统分析，揭示了周期轨道由流动过程中能量耗散与跳跃中恢复的能量之间的平衡所产生，并利用混合Lyapunov工具研究其稳定性，满足混合基本条件可保证渐近稳定的鲁棒性。
摘要：
我们研究了由重置反馈诱导的渐近稳定的周期轨迹的存在性。该分析针对平面系统进行。将问题转化为混合设置，我们展示周期轨道由流动过程中耗散的能量与跳跃中恢复的能量之间的平衡产生。通过混合Lyapunov工具研究周期轨道的稳定性。满足所谓的混合基本条件确保了渐近稳定的鲁棒性。讨论了该方法扩展到更一般机械系统的情况。
英文摘要：
We study the existence of asymptotically stable periodic trajectories induced by reset feedback. The analysis is developed for a planar system. Casting the problem into the hybrid setting, we show that a periodic orbit arises from the balance between the energy dissipated during flows and the energy restored by resets, at jumps. The stability of the periodic orbit is studied with hybrid Lyapunov tools. The satisfaction of the so-called hybrid basic conditions ensures the robustness of the asymptotic stability. Extensions of the approach to more general mechanical systems are discussed.
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