The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we investigate the frequency-weighted $\mathcal{H}_2$-pseudo-optimal model order reduction problem wherein a subset of the optimality conditions for the local optimum is attempted to be satisfied. We propose two iteration-free algorithms, for the single-sided frequency-weighted case of $\mathcal{H}_2$-model reduction, where a subset of the optimality conditions is ensured by the reduced system. In addition, the reduced systems retain the stability property of the original system. We also present an iterative algorithm for the double-sided frequency-weighted case, which constructs a reduced-order model that tends to satisfy a subset of the first-order optimality conditions for the local optimum. The proposed algorithm is computationally efficient as compared to the existing algorithms. We validate the theory developed in this paper on three numerical examples.

中文翻译：

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频率加权ℌ2-伪最优模型降阶

频率加权模型降阶技术用于找到在频率权重强调的频率区域内表现出高保真度的高阶系统的低阶近似。在本文中，我们研究了频率加权 $\mathcal{H}_2$-伪最优模型降阶问题，其中试图满足局部最优的最优条件的子集。我们提出了两种无迭代算法，用于$\mathcal{H}_2$-模型缩减的单边频率加权情况，其中优化条件的子集由缩减系统确保。此外，简化后的系统保留了原系统的稳定性。我们还提出了一种双面频率加权情况的迭代算法，它构造了一个降阶模型，该模型倾向于满足局部最优的一阶最优条件的子集。与现有算法相比，所提出的算法在计算上是有效的。我们通过三个数值例子验证了本文提出的理论。