Existence of discrete state estimators for hybrid systems on a lattice

The observability properties of a class of hybrid systems whose continuous variables are available for measurement are considered. We show that the discrete variable 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. It updates two variables at each step, the upper and lower bound of the set of all possible discrete variable values compatible with the output sequence. Causes of the estimator complexity are investigated.