In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-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 $\mathcal{H}_2\otimes\mathcal{L}_2$-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.

翻译：在本文中,我们将现有的 $\ mathcal{H%2\ otimes\ mathcal{L ⁇ 2$- 最佳模式排序框架概括为广泛的参数线性时间变异系统。 为此,我们为一组结构化减序模型得出头等必要微量条件,然后在此基础上,提出一种基于稳定性- 保留优化的方法,用于计算本地的 $\ mathcal{H ⁇ 2\ otimes\ mathcal{L ⁇ 2$- 最优减序模型。我们还从理论上比较文献和数字实验中的现有方法,表明我们的新方法如何以合理的计算努力产生稳定的优化减序模型,而近似误差则明显较低。