Recent results on nonlinear model matching

The purpose of this paper was a review of some recent results dealing with the problem of matching a prescribed nonlinear input-output behavior via dynamic state feedback. It has been shown that, under appropriate hypotheses, the solvability of a model matching problem can be expressed in terms of properties of a suitable controlled invariant distribution. Those properties have been related to the infinite zero structures of the process and the model. Then, the case in which the plant can be made linear, from an input-output point of view, via a static state feedback, and the model is linear has been discussed. In that case, it has been shown that the infinite zero structure can be computed directly on the coefficients of the Taylor-series expansion of the first-order Volterra kernels. This simplifies the test for the existence of a solution of the model matching problem.