In this paper, we compute a low order approximation of a system of large order $n$ that matches $ν$ moments of order $j_i$ of the transfer function, at $ν$ interpolation points, has $\ell$ poles and $k$ zeros fixed and also matches $ν-(\ell +k)$ moments of order $j_i+1$, where $j_i+1$ is the multiplicity of the $i$-th interpolation point. We derive explicit linear systems in the free parameters to simultaneously achieve the required pole-zero placement and match the desired high order moments. We compute the closed form of the free parameters that meet the constraints, as the solution of a $ν$ order linear system. Furthermore, for data-driven model reduction, we generalize the construction of the Loewner matrices to include the data and the imposed pole and higher order moment constraints. The resulting approximations achieve a trade-off between the good norm approximation and the preservation of the dynamics of the original system in a region of interest.
Pole Placement Approach to Coherent Passive Reservoir Engineering for Storing Quantum Information
The Australian National University（澳大利亚国立大学）；INRIA Paris（法国国家信息与自动化研究所巴黎分部）；Zhejiang University（浙江大学）；CNRS, Laboratoire des signaux et systèmes (L2S), CentraleSupélec（法国国家科学研究中心信号与系统实验室（L2S），中央理工-高等电力学院）；University of New South Wales at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防军学院）
Time-Domain Moment Matching for Second-Order Systems [Extended Version]
Wageningen University & Research（瓦赫宁根大学与研究中心）；Politehnica University of Bucharest（布加勒斯特理工大学）；”Gheorghe-Mihoc–Caius Iacob” Institute of Statistical Mathematics and Applied Mathematics of the Romanian Academy（罗马尼亚科学院“格奥尔基-米霍克-卡伊乌斯·亚各布”统计数学与应用数学研究所）
