Results on stability and robustness of hybrid limit cycles for a class of hybrid systems

This work addresses stability and robustness properties of hybrid limit cycles for a class of hybrid systems, which combine continuous dynamics on a flow set and discrete dynamics on a jump set. Under some mild assumptions, we show that the stability of hybrid limit cycles for a hybrid system is equivalent to the stability of a fixed point of the associated Poincaré map. As a difference to related efforts for systems with impulsive effects, we also explore conditions under which the stability properties of the hybrid limit cycles are robust to small perturbations. The spiking Izhikevich neuron is presented to illustrate the notions and results throughout the paper.