Modelling mode-switching systems as the limit of discrete computational processes

This paper presents a theoretical outline of a new formalism for mode switching or hybrid systems in which continuous dynamics are represented as the limit of a discrete computational process. Mode switching systems are systems which are composed of continuous modes switched between by discrete transitions. Most existing mode switching formalisms treat their continuous and discrete components as distinct types of process. This new approach brings the two together and provides a platform for the investigation of the transition between continuous change and discrete events.