Implicit and Explicit Matching of Non-Proper Transfer Functions in the Loewner Framework

The reduced-order modeling of a system from data is an established task in system and control theory and well understood for standard linear systems with the Loewner framework being one of many prolific approaches. While there is significant overlap between this problem and that of system identification, in particular, the latter does not immediately imply that model order reduction is occurring. In the case of descriptor systems for which the transfer function is not a proper rational function anymore, recent research efforts have addressed strategies to deal with the non-proper parts more or less explicitly. In this work, we propose a variant of a Loewner matrix-based interpolation algorithm that implicitly addresses possibly non-proper components of the system response. We evaluate the performance of the suggested approach by comparing against recently-developed explicit algorithms for which we propose a linearized Navier-Stokes model with a significant non-proper behavior as a benchmark example.