Hybrid systems as a topological abstraction of digitally controlled systems

Starting from a system theory of digitally controlled systems, we define computable control laws. After recalling classical undecidability results, we focus on the notion of "cell decomposition", defined as an oracle partitioning the space of input-output trajectories and show how this notion solves the previous undecidability. The key issue is that the cell decomposition induces a natural hybrid system model of the initial system.