In this paper, we study asymptotically stable sets of non-autonomous discrete dynamical systems. Some basic concepts are introduced for non-autonomous discrete systems, including w-limit set, Lypunov stable set, and asymptotically stable set. We give some sufficient conditions for non-autonomous discrete dynamical systems to have asymptotically stable sets.

non-autonomous discrete dynamical systems, w-limit set, Lyapunov stable set, asymptotically stable set.