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In this paper hybrid systems with discrete-event measurements and inputs are considered. Such systems consist of a continuous-variable subsystem and a discrete-event subsystem which are connected in a closed loop. Stochastic automata are used as models of the discrete-event behavior of the hybrid system, which is in general non-deterministic. It is shown that the model can be set up by, first, modeling the discrete-event behavior of the continuous-variable subsystem by means of a stochastic automaton. It is shown, that the transition relation of this automaton can be derived from a continuous-variable description of the subsystem. Second, the resulting model is combined with the model of the discrete-event subsystem, which in general can be represented by a deterministic automaton. As the continuous-variable subsystem and, therefore, also the hybrid system cannot be modeled exactly by an automaton, the model of the hybrid system generates spurious solutions. Therefore, conditions on the model of the continuous-variable and on the model of the hybrid system will be presented which yield the best complete model of the hybrid system, i.e., the model which generates all event sequences which may occur in the hybrid system and the least number of spurious solutions.
Lunze et al. (Sat,) studied this question.