Global results on reset-induced periodic trajectories of planar systems
Systems and Control
2021-02-26 v1 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1509.06992,
title = {Global results on reset-induced periodic trajectories of planar systems},
author = {Andrea Bisoffi and Fulvio Forni and Mauro Da Lio and Luca Zaccarian},
journal= {arXiv preprint arXiv:1509.06992},
year = {2021}
}
Comments
7 pages, 16 figures