We present a novel model-order reduction (MOR) method for linear time-invariant systems that preserves passivity and is thus suited for structure-preserving MOR for port-Hamiltonian (pH) systems. Our algorithm exploits the well-known spectral factorization of the Popov function by a solution of the Kalman-Yakubovich-Popov (KYP) inequality. It performs MOR directly on the spectral factor inheriting the original system's sparsity enabling MOR in a large-scale context. Our analysis reveals that the spectral factorization corresponding to the minimal solution of an associated algebraic Riccati equation is preferable from a model reduction perspective and benefits pH-preserving MOR methods such as a modified version of the iterative rational Krylov algorithm (IRKA). Numerical examples demonstrate that our approach can produce high-fidelity reduced-order models close to (unstructured) $\mathcal{H}_2$-optimal reduced-order models.

翻译：我们为线性时变系统提出了一种新型模式-减少命令方法,该方法保存了被动性,因此适合港口-汉堡(pH)系统的结构保护MOR。我们的算法利用了通过Kalman-Yakubovich-Popov(KYP)不平等的解决办法而众所周知的波波波夫函数的光谱因子化。它直接在光谱因子上进行MOR,该光谱因子继承了原系统的宽度,在大范围内使摩尔能够产生。我们的分析表明,从模型减少角度来说,与相关的代数里卡提方程式最低溶法相对应的光谱因子化是可取的,并且有利于pH-保护摩尔法的方法,例如互动理性Krylov算(IRKA)的修改版本。数字实例表明,我们的方法可以产生接近(无结构的) $mathcal{H ⁇ 2$-optimal 降序模型的高不灵的减序模型。