Design of O(ε) dwell-time graph for stability of singularly perturbed hybrid linear systems

The paper deals with singularly perturbed hybrid systems. It proposes a methodology for building a graph defining all the rules that ensure the origin is a stable equilibrium in presence of a dwell-time of order of the parameter defining the ratio between the two time-scales of the system. In this framework one can also treat the corresponding problem for interesting particular cases such as: singularly perturbed switched linear systems without impulses, one scale hybrid systems or one scale switched systems. A numerical example illustrates the theoretical results completing the paper.