On p-normal forms of nonlinear systems

Using the differential-geometric control theory, we present in this note a necessary and sufficient condition under which an affine system is locally feedback equivalent to, via a change of coordinates and restricted smooth state feedback, a generalized normal form called p-normal form, which includes Brunovsky canonical form and feedback linearizable systems in a lower-triangular form as its special cases. We also give an algorithm for computing the appropriate coordinate transformations and feedback control laws.