X. Nicollin, A. Olivero, J. Sifakis, S. Yovine, "An Approach to the Description and Analysis of Hybrid Systems," in Robert L. Grossman, Anil Nerode, Anders P. Ravn, Hans Rischel, eds., Hybrid Systems, Springer-Verlag, 1993


Between two successive transitions the temperature changes according to laws that depend on the current state (heater is ON or OFF) and that describe its evolution as a function of its initial value and the time spent in the state.

Fig 1. shows the evolution of the system as an alternation of ON and OFF steps, each step composed of a continuous state transformation followed by a transition.

This paper proposes a semantics of the model in terms of labeled transition systems with two types of labels: (1) actions, which are the names of discrete state changes, and (2) non-negative real numbers representing the time elapsed. These transition systems have features that take into account the assumptions made about the nature of time.