  In this work, the problem of designing observers for estimating a single
nonlinear functional of the state is formulated for general nonlinear systems.
Notions of functional observer linearization are also formulated, in terms
achieving exactly linear error dynamics in transformed coordinates and with
prescribed rate of decay of the error. Necessary and sufficient conditions for
the existence of a lower-order functional observer with linear dynamics are
derived. The results provide a direct generalization of Luenberger's linear
theory of functional observers to nonlinear systems.
