Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially profound in many high-tech systems, in which logic-based components, digital networks and embedded controllers are combined with continuous physical processes. As these high-tech systems are becoming increasingly complex there is a strong need for a rigorous hybrid systems theory that allows the modeling, analysis and design of systems in which logic-based elements and continuous processes interact. Basically, models for hybrid systems consist of some form of differential or difference equations (to describe the continuous part) on the one hand and automata or other discrete-event models (to describe the logic part) on the other. A simple example is the regulation of the temperature in a room by an embedded controller named the thermostat. This is a system that can operate in two modes: “on” and “off”. In each mode of operation the evolution of the temperature T can be described by a different differential equation.
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