Design of reduced-order observers of nonlinear systems through change of coordinates

We extend our recent results (2001, 2002) to the design of reduced-order observers for nonlinear systems. The approach method is to use the change of coordinates, which is based on the solution of a system of first-order nonlinear PDEs. The sufficient condition for the solution of the PDEs is provided under very general conditions. The approach is also applicable when the system is only detectable. The method proposed in this paper is constructive and can be applied approximately to any sufficiently smooth, linearly observable system yielding a local observer with approximately linear error dynamics.