A behavioral approach to model reduction

The behavioral approach to exact modeling leads to the concept of generating systems or MPUM´s (most powerful models). It turns out that all exact models of a given data set, are parametrized by means of a cascade interconnection of generating systems with an arbitrary system. A model reduction scheme is proposed where the reduced order model is generated by retaining some of the elements of this cascade interconnection. It follows that under certain conditions, this approach provides a controller which stabilizes both the reduced as well as the full order models