Control in o-minimal Hybrid Systems

In this paper, we consider the control of general hybrid systems. In this context we show that time-abstract bisimulation is not adequate for solving such a problem. That is why we consider other equivalence, namely the suffix equivalence based on the encoding of trajectories through words. We show that this suffix equivalence is in general a correct abstraction for control problems. We apply this result to o-minimal hybrid systems, and get decidability and computability results in this framework