Hybrid systems modelers have become the corner stone of embedded system development, with Simulink a de facto standard and Modelica a new player. Such tools still raise a number of issues that, we believe, require more fundamental understanding. In this paper we propose using non standard analysis as a semantic domain for hybrid systems—non standard analysis is an extension of classical analysis in which infinitesimals (the epsilon and eta in the celebrated generic sentence "for all epsilon there exists eta..." in college maths) can be manipulated as first class citizens. This allows us to provide a denotational semantics and a constructive semantics for hybrid systems, thus establishing simulation engines on a firm mathematical basis. In passing, we cleanly separate the job of the numerical analyst (solving differential equations) from that of the computer scientist (generating execution schemes).

Keywords : hybrid systems, hybrid systems modelers, modeling, non-standard analysis

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