Constrained rational fitting for $$\mathcal {D}$$-stable model order reduction

Abstract A classical problem in data-driven model order reduction (MOR) of linear time-invariant (LTI) systems is the preservation of structural properties of the underlying large-scale dynamics. When dealing with MOR based on transfer function measurements, one relevant problem is how to force the reduced-order model (ROM) to inherit the asymptotic stability of the reference system, i.e., to enforce the poles of the ROM transfer function to have strictly negative real part. In this work, we tackle the more general problem of placing such poles in arbitrary linear matrix inequality (LMI) regions of the complex plane, which include a rich class of convex sets symmetric with respect to the real axis. LTI systems with poles constrained to this kind of regions are called $$\mathcal {D}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> </mml:math> -stable. Combining well-established results from control theory and recent developments in asymptotically stable rational approximation algorithms, we show that the problem can be solved efficiently via standard convex optimization routines. Several numerical testbenches of engineering interest confirm the effectiveness of the proposed methodology in practical applications.