Abstract
In this paper, a necessary and sufficient condition for dynamic feedback linearizability by endogenous feedback of control-affine nonlinear systems is presented. The condition is based on a modified derived flag of a Pfaffian system associated with a control system which takes into account the presence of a precompensator. It is shown that the generators associated with this modified derived flag must satisfy a number of congruences. The congruences ensure that the conditions of the GS algorithm are satisfied for the prolongated system and thus provide an algorithm to calculate the required feedback and state space transformations. A tower structure is identified with respect to a set of indices corresponding to a set of generalized Kronecker indices. Using these conditions, a bound related to the extent of precompensation required for each input channel is obtained. It is shown how linearizing outputs can be identified by studying the derived flag of the Pfaffian system associated with a nonlinear system.
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