Near-optimal Frequency-weighted Interpolatory Model Reduction

This paper develops an interpolatory framework for weighted-H2 model reduction of MIMO dynamical systems. A new representation of the weighted-H2 inner products in MIMO settings is introduced and used to derive associated first-order necessary conditions satisfied by optimal weighted-H2 reduced-order models. Equivalence of these new interpolatory conditions with earlier Riccati-based conditions given by Halevi is also shown. An examination of realizations for equivalent weighted-H2 systems leads then to an algorithm that remains tractable for large state-space dimension. Several numerical examples illustrate the effectiveness of this approach and its competitiveness with Frequency Weighted Balanced Truncation and an earlier interpolatory approach, the Weighted Iterative Rational Krylov Algorithm.