The control of smooth input-affine nonlinear systems can be performed using exact linearization techniques which are based on the existence of a fictitious output map producing a (nonlinear) relative degree equal to the system order. A method is proposed on how to explicitly construct a map having the desired properties for a special class of nonlinear systems. This class is obtained by taking into account only the linear and quadratic part of the drift vector and the constant and linear part of the input vector of a general nonlinear system and can be thought of as a better approximation of that system than the usual linear or bilinear approaches. One important fact presented is that under some additional assumptions on the higher-order terms more general results are obtainable than those obtained by the well-known matching conditions.
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