A polynomial approach to a nonlinear model matching problem

The paper studies the model matching problem for nonlinear systems, described by a higher order input-output differential equation, not necessarily realizable in the state-space form. Only the feedforward solution is looked for. The problem statement and solution rely on the recently introduced concept of a generalized transfer function for nonlinear systems. We require that the transfer functions of the compensated system and that of the prespecified model be equal, like in the linear case. However, in the nonlinear transfer function formalism one does not work with equations but with differential one-forms, and the existence of the compensator is restricted by integrability of the one-form corresponding to the compensator. Necessary and sufficient but nonconstructive solvability conditions are given. The second theorem lists a number of different (constructive) conditions under which the one-form is integrable. Additional freedom is sometimes obtained by forcing the conditions of the second theorem to hold via introducing assumptions suggested by the Euclidean division algorithm.