Balancing for nonlinear systems

We present a method of balancing for nonlinear systems which is an extension of balancing for linear systems in the sense that it is basd on the input and output energy of a system. It is a local result, but gives `broader¿ results than we obtain by just linearizing the system. Furthermore, the relation with balancing of the linearization is dealt with. We propose to use the method as a tool for nonlinear model reduction and investigate some of the properties of the reduced system