Observability of a Class of Hybrid Systems on Bounded Lattices

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Domitilla Del Vecchio and Richard M. Murray
Submitted, 2004 Conference on Decision and Control (CDC)

The observability properties of a class of hybrid systems whose continuous variables are available for measurement are considered. We show that the discrete variables' dynamics can be always extended for observable systems to a lattice in such a way that the extended system has the properties that allow the construction of the LU discrete state estimator. Such an estimator updates two variables at each step, namely the upper and lower bound of the set of all possible discrete variables' values compatible with the output sequence. We give an estimate of the complexity of the estimator in the worst case.