A CONDITION FOR DYNAMIC FEEDBACK LINEARIZATION OF CONTROL-AFFINE NONLINEAR-SYSTEMS

In this paper, a necessary and sufficient condition for dynamic feedba ck linearizability by endogenous feedback of control-affine nonlinear systems is presented. The condition is based on a modified derived fla g of a Pfaffian system associated with a control system which takes in to account the presence of a precompensator. It is shown that the gene rators associated with this modified derived flag must satisfy a numbe r of congruences. The congruences ensure that the conditions of the GS algorithm are satisfied for the prolongated system and thus provide a n algorithm to calculate the required feedback and state space transfo rmations. A tower structure is identified with respect to a set of ind ices corresponding to a set of generalized Kronecker indices. Using th ese conditions, a bound related to the extent of precompensation requi red for each input channel is obtained. It is shown how linearizing ou tputs can be identified by studying the derived flag of the Pfaffian s ystem associated with a nonlinear system.