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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 4.2

The state partitioning problem of

quantised systems

Jan Lunze

Institute of Automation and Computer Control

Ruhr-University Bochum

D-44780 Bochum

Germany

Lunze@esr.ruhr-uni-bochum.de

1 DESCRIPTION OF THE PROBLEM

Consider a continuous system whose state can only be accessed through a quantizer. The quantizer is defined by a partition of the state space. The system generates an event if the system trajectory crosses the boundary between adjacent partitions.

The problem concerns the prediction of the event sequence generated by the system for a given initial event. As the initial event does not define the initial system state unambiguously but only restricts the initial state to a partition boundary, when predicting the system behavior ...

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