Local nonlinear model matching: from linearity to nonlinearity

The model matching problem consists of designing a compensator for a given system, called the plant, in such a way that the resulting input-output behaviour matches that of a prespecified model. In this paper a local solution of the nonlinear model matching problem is given for the case that the model is decouplable by static state feedback. The main theorem states that under generic conditions on the plant the problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model. The generic conditions are identified. They naturally appear in the solution of the dynamic input-output decoupling problem for the plant. The theory is illustrated by means of two examples