A necessary and sufficient condition for the existence of a nonlinear observer with linearizable error dynamics

Abstract

We provide a necessary and sufficient condition for the existence of nonlinear observer with linearizable error dynamics. The result is applicable to any real analytic observable nonlinear system. The necessary and sufficient condition is the solvability of a first-order nonlinear partial differential equation (PDE). The solution yields a change of state coordinates which linearizes the error dynamics. Under very general conditions, the existence and uniqueness of the solution is proved. Siegel's theorem is obtained as a corollary. The technique is constructive and yields a method for constructing approximate solutions.