On Functional Observability of Nonlinear Systems and the Design of Functional Observers with Assignable Error Dynamics

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 first derived, leading to functional relationships between the Lie derivatives of the output to be estimated and the ones of the measured output. These are directly used in the proposed design of the functional observer. The functional observer is defined in differential input-output form, satisfying an appropriate invariance condition that emerges from the state-space invariance conditions of the literature. A concept of functional observer index is also proposed, to characterize the lowest feasible order of functional observer with pole assignment. Two chemical reactor applications are used to illustrate the proposed approach.