Global results on reset-induced periodic trajectories of planar systems
Provides theoretical foundations for reset-induced oscillations in planar systems, with potential extensions to broader mechanical systems.
The paper proves existence and asymptotic stability of periodic trajectories in planar reset feedback systems, using hybrid Lyapunov methods and showing robustness under hybrid basic conditions.
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.