Optimization-Based Parametric Model Order Reduction Via <i>H</i>₂ ⊗ <i>L</i>₂ First-Order Necessary Conditions

Abstract

In this paper, we generalize existing frameworks for H2 ⊗ L2-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary optimality conditions for a class of structured reduced-order models and then, building on those, propose a stability-preserving optimization-based method for computing locally H2 ⊗ L2-optimal reduced-order models. We also make a theoretical comparison to existing approaches in the literature and, in numerical experiments, show how our new method, with reasonable computational effort, produces stable optimized reduced-order models with significantly lower approximation errors.