An implementation of hybrid specification with discrete event controllers -2D system theoretic approach in a behavioral framework-

In this paper, we consider an implementability of hybrid dynamical systems in a behavioral framework. Here, we regard hybrid dynamical systems as a class of systems whose dynamics evolve with two different types of independent variables, one is a ldquotimerdquo with which a solution of differential or difference equations evolve, other is ldquothe event timerdquo or ldquodiscrete state indexrdquo corresponding to the occurrence of a discrete event or a switching time between one and another states. Such a stand point enables us to see that a hybrid system is viewed as a 2-dimensional (which is abbreviated to as 2D) dynamical system. In this new setting, we provide a necessary and sufficient condition of the existence of a event-driven controller for a given hybrid specification to be controlled.