Model reduction by moment matching for nonlinear systems

The problem of model reduction by moment matching for nonlinear systems is addressed and solved using the recently introduced notion of moment for nonlinear systems. It is shown that reduced order models can be parameterized by a free mapping which, in turn, can be used so that the model possesses specific properties, e.g. it has an asymptotically stable equilibrium or given relative degree, it is minimum phase, it is passive. In addition, a nonlinear enhancement of the notion of Markov parameters is provided. The theory is illustrated by means of simple examples.