Functional observers for nonlinear systems

In this work, the problem of designing functional observers is formulated for general nonlinear systems, for a single output to be estimated and a single measured output. Notions of functional observer linearization are also formulated, in the sense of achieving linear error dynamics in transformed coordinates with prescribed rate of decay of the error. Necessary and sufficient conditions for the existence of a lower-order functional observer with linear dynamics and linear output map are derived.