Model reduction of nonlinear systems with bounded incremental $L_2$ gain

A model reduction procedure for a class of nonlinear systems is presented in the current paper. Nonlinear systems are considered that can be decomposed into a linear subsystem of high order and a nonlinear subsystem of relatively low order, allowing for an approach in which only the linear subsystem is reduced using well-developed linear model reduction techniques. For this approach, conditions for stability of the reduced-order nonlinear system are given, as well as an error bound in terms of the L 2 signal norm. Herein, the nonlinear subsystem is assumed to have a bounded incremental L 2 gain, which proves to be a crucial property in the derivation of the results. The method is illustrated by means of an example.