We re-examine the basic hybrid control set-up of a continuous plant in a closed feedback loop with a finite state control automaton and an interface consisting of an A/D map and a D/A map. We address the question of how dynamic specifications can be formulated independently of a particular A/D map, and of the effect of refining an A/D map. The main contribution of this paper is that it extends the framework of supervisory controller synthesis for hybrid systems to include more general dynamic specifications, and demonstrates how to employ known results to solve these synthesis problems.
