The Loewner framework and transfer functions of singular/rectangular systems

A connection is established between the Loewner framework for model reduction and the generalized inverses of singular and rectangular matrices. In this context both the Moore–Penrose and the Drazin inverses are involved. As a consequence this approach yields transfer functions for singular and rectangular systems. Thus the Loewner framework constitutes a natural and direct way for constructing models from measured input/output data.