A deadbeat function observer is an estimator that estimates exactly a linear function of the state of a deterministic discrete-time linear system via an incomplete state observation. Structural properties of such deadbeat function observers are studied by a geometric approach. The main result is the derivation of the minimal order of deadbeat function observers, which has been a longstanding open problem. The result reveals a fundamental relation between the observer order and the number of exogenous data required for exact estimation. An upper bound for the minimal order, which is at the same time the minimal order for generic cases, is derived in terms of the observability indices of the plant. A simple design algorithm of a minimal-time minimal-order function observer is also derived. Some numerical examples are also discussed.
