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In this paper, we generalize existing frameworks for$\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broadclass of parametric linear time-invariant systems. To this end, we derivefirst-order necessary ptimality conditions for a class of structuredreduced-order models, and then building on those, propose astability-preserving optimization-based method for computing locally$\mathcal{H}_2\otimes\mathcal{L}_2$-optimal reduced-order models. We also makea theoretical comparison to existing approaches in the literature, and innumerical experiments, show how our new method, with reasonable computationaleffort, produces stable optimized reduced-order models with significantly lowerapproximation errors.

Optimization-based parametric model order reduction via $\mathcal{H}_2\otimes\mathcal{L}_2$ first-order necessary conditions