A timed discrete-event abstraction of continuous-variable systems

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Abstract
The paper concerns continuous-variable systems whose state can only be observed through a quantizer, which indicates the time instant and the direction of the change of the quantized state value. These changes are considered as events. The problem is to find a concise representation of the quantized system, which allows to determine for a given initial event all timed event sequences that the quantized system can generate. Since the quantized system does not possess the Markov property, the modelling aim is to find a semi-Markov process which describes a superset of the event sequences of the quantized system. The paper shows how such a semi-Markov process can be obtained for a given quantized system. The model provides information about the occurrence time of the events and about the probability of the occurrence. The modelling problem and its solution are illustrated by considering a quantized oscillator.

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