A unified approach for studying discrete and continuous dynamical systems

The goal of the paper is to present discrete transition systems and continuous dynamical systems in a uniform manner, stressing the fundamental differences as well as the commonalities between these two fundamental models. Such a framework seems to be a pre-requisite to any theory and methodology for hybrid systems. For both types of systems we introduce three models (a closed system, a system with one type of input, and a system with two types of input) such that the problems associated with them correspond respectively to the tasks of simulation, verification and control synthesis. We discuss some of the computational problems associated with building control CAD tools that out carry these tasks