An extended linearization approach to nonlinear system inversion

The inversion problem for nonlinear systems is considered from both the internal viewpoint (state-equation representations) and the external viewpoint (Volterra-series representations). In order to circumvent difficulties in the known, exact inversion theory, a method for obtaining what will be called a partial inverse system is proposed. For a given nonlinear system, a cascade system, typically containing differentiators, is found such that the overall nonlinear system has a family of constant operating points with inputs and outputs identical. Furthermore, the linearization of the overall system about each of these constant operating points is the identity system.