Morse decompositions for periodic general dynamical systems and differential inclusions (Q1928757)

In this paper, the authors define a Morse decomposition for invariant sets of a periodic general dynamical system (i.e., a periodic multivalued dynamical system) using the standard approach -- constructing a sequence of uniform attractor-repeller pairs -- and prove the robustness of such a decomposition under small perturbations. The result obtained can then be applied to non-autonomous differential inclusions with only upper-semicontinuous right-hand side. As a concrete application, the authors study the effect of small time delays on the asymptotic behaviour of control systems.