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Systematic development of hybrid systems

Hybrid embedded systems are systems that are characterized by involving discrete as well as continuous dynamics, such as digital software interacting with an analog environment. In the design of such systems, different time models and techniques from different disciplines---mainly computer science and control theory---are usually employed. An isolated consideration of the discrete and continuous parts of a hybrid system already at the beginning of the development process together with imprecisely defined interaction between these parts can lead to inappropriate or incorrect designs. Therefore, this thesis introduces formal, integrated notations and development techniques for hybrid systems which support development processes that postpone this partitioning of a hybrid system to the later development phases.The introduced notations for data-flow and control-flow in hybrid systems precisely define the interaction of discrete and continuous dynamics in a hybrid system. They are visual and modular, and can be used for environment modeling, requirements analysis and specification of hybrid systems. For these notations, the thesis defines refinement techniques as transformations of the hybrid models. The techniques introduced aim at moving from an abstract model based on a dense time scale to a model with more detailed timing constraints that operates in discrete time. They are defined such that they can be used together with methods from numerical mathematics and control theory.Further motivation for the refinement techniques stems from a formalization and classification of the properties required of hybrid systems. The classification reveals that trace inclusion is a suitable refinement notion for most central properties of hybrid systems. Furthermore, the detailed study of the properties and some of their proof methods, as contained in the thesis, fosters a better understanding of hybrid systems by computer scientists and formalizes parallels between computer science and control theory.For all introduced elements of a design methodology for hybrid systems the thesis identifies their position and potential within the development process of hybrid systems.