Preprint 10-2019

Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems

Author(s) : Christopher A. Beattie , Serkan Gugercin , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2019

MSC 2000

34H05 Control problems

65L70 Error bounds

Abstract :
We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and take advantage of the underlying structural features of the system. We introduce approaches that incorporate regularization together with prudent selection of interpolation data. We focus on linear time-invariant systems and present a systematic treatment of a variety of model classes that include combinations of index-$1$ and index-$2$ systems, describing in particular how constraints may be represented in the transfer function and then preserved with interpolatory methods. We propose an algorithm to generate effective interpolation data and illustrate its effectiveness on a %two numerical example.

Keywords : port-Hamiltonian system, positive-real system, model reduction, differential-agebraic system