Homogeneous hybrid systems and a converse Lyapunov theorem

In this paper we introduce homogeneity for hybrid systems (using generalized dilations) and provide basic implications of this property similar to that of continuous-time and discrete-time homogeneous systems. In our main result we state that stability of a hybrid system that is robust with respect to small perturbations implies the existence of a homogeneous Lyapunov function for the system. This converse Lyapunov theorem unifies the previous results