Optimization-based parametric model order reduction via ℋ_2⊗ℒ_2 first-order necessary conditions
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In this paper, we generalize existing frameworks for ℋ_2⊗ℒ_2-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality conditions for a class of structured reduced-order models, and then building on those, propose a stability-preserving optimization-based method for computing locally ℋ_2⊗ℒ_2-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.
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