Abstract
In order to promote a deeper understanding of hybrid, i.e. mixed discrete and continuous, systems, we introduce a set of important properties of such systems and classify them. For the properties of stability and attraction which are central for continuous systems we discuss their relationship to discrete systems usually studied in computer science. An essential result is that the meaning of these properties for discrete systems vitally depends on the used topologies. Based on the classification we discuss the utility of a refinement notion based on trace inclusion. Furthermore, for proofs of stability the role of Liapunov functions as abstractions is emphasized by identifying conditions under which they define Galois connections.
This work was supported with funds of the DFG under reference number Br 887/9 within the priority program Design and design methodology of embedded systems.
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Stauner, T. (2001). Hybrid Systems’ Properties — Classification and Relation to Computer Science. In: Moreno-Díaz, R., Buchberger, B., Luis Freire, J. (eds) Computer Aided Systems Theory — EUROCAST 2001. EUROCAST 2001. Lecture Notes in Computer Science, vol 2178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45654-6_7
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DOI: https://doi.org/10.1007/3-540-45654-6_7
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