A method to design functional observers - dynamic systems that estimate a specified function of a plant's state rather than the full state - for nonlinear systems directly in differential input-output form. Local functional observability is characterized as functional relationships between the Lie derivatives of the measured output and those of the output to be estimated, and these relationships are used to build an observer whose estimation error obeys linear dynamics with arbitrarily assignable poles. A functional observer index is introduced to characterize the lowest feasible observer order, and the construction specializes to the classical Luenberger result for linear systems.
This paper proposes a novel approach for designing functional observers for nonlinear systems, with linear error dynamics and assignable poles. Sufficient conditions for functional observability are …