Preserving the DAE structure in the Loewner model reduction and identification framework

Abstract

We propose an extension of the Loewner framework to descriptor linear systems that preserves the DAE (differential algebraic equation) structure of the underlying system. More precisely, by means of post-processing the data, the behavior at infinity is matched. As it turns out, the conventional procedure constructs a reduced model by directly compressing the data and hence losing information at infinity. By transforming the matrix pencil composed of the E and A matrices into a generalized block diagonal form, we can separate the descriptor system into two subsystems; one corresponding to the polynomial part and the other to the strictly proper part of the transfer function. Different algorithms are implemented to transform the matrix pencil into block diagonal form. Furthermore, a data-driven splitting of the descriptor system can be achieved in the Loewner framework. Hence, the coefficients of the polynomial part can be estimated directly from data. Several numerical examples are presented to illustrate the theoretical discussion.