  Hybrid systems with memory are dynamical systems exhibiting both hybrid and
delay phenomena. In this note, we study the asymptotic stability of hybrid
systems with memory using generalized concepts of solutions. These generalized
solutions, motivated by studying robustness and well-posedness of such systems,
are defined on hybrid time domains and parameterized by both continuous and
discrete time. We establish Lyapunov-based sufficient conditions for asymptotic
stability using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii
functionals. Examples are provided to illustrate these conditions.
