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 that is nonregular static feedback linearizable but is not regular dynamic feedback linearizable. Then we present some preliminary necessary conditions as well as sufficient conditions for nonregular feedback linearization. The sufficient conditions are checkable, and if they are verified, a linearizing feedback could be calculated following a recursive procedure, provided that the integrations of a set of completely integrable systems are available. (C) 1997 Elsevier Science Ltd.