On the approximation to dynamic systems

This paper presents a sufficient condition for obtaining a dynamic approximation to the normal form which can be used to obtain the same feedback linearization while its internal dynamics keep the same features of stability than those of the zero dynamics. This dynamic approximation is achieved by finding the polynomial approximations to the solution of an ordinary differential equation that solves a set of partial differential equations whose solutions in turn are used to obtain the diffeomorphism for getting the normal form.