An approximate nonlinear observer with polynomial coordinate transformation maps

The state equivalence condition to the nonlinear observer form is stated in terms of the exactness of one-form. Using the definition of the approximate closedness, we relax the equivalence condition, thereby obtaining a necessary and sufficient condition for the approximate observer error linearizability. This approximate observer theory extends the realm of applications. Another great advantage of this approximation method is that the coordinate transformation is directly obtainable as vectors of polynomials, while it is, in general, not possible with the existing method,.