Abstract This chapter briefly highlights how one might address the aforementioned topological obstructions. We discuss almost global stabilization , periodic time-varying feedback and broadest most successful framework for discontinuous feedback: hybrid control theory .

We study finite automata running over infinite binary trees. A run of such an automaton is usually said to be accepting if all its branches are accepting. In this article, we relax the notion of accepting run by allowing a certain quantity of rejecting branches. More precisely we study the following criteria for a run to be accepting: (i) it contains at most finitely (resp. countably) many reje...