On Nonregular Feedback Linearization

This paper investigates the use of nonregular (not necessarily regular) static/dynamic state feedbacks to achieve feedback linearization of affine nonlinear systems. First, we provide an example which is nonregular static feedback linearizable but is not regular dynamic feedback linearizable. Then, we present some necessary conditions as well as sufficient conditions for nonregular feedback linearization. The sufficient conditions are checkable, and if they are verified, a linearing–feedback could be calculated following a recursive procedure, provided the integrations of a set of completely integrable systems are available.