In this paper, we consider structure-preserving model reduction for multi-input multi-output port-Hamiltonian systems based on projection. Specifically, we prove that the reduced system, the projection matrix of which is constructed by solving specific Sylvester equations, satisfies the right (or left) tangential interpolation condition and retains the port-Hamiltonian structure; hence it remains passive. Based on the tangential interpolation, we propose two structure-preserving model reduction algorithms for port-Hamiltonian systems and present several numerical examples to illustrate their effectiveness.

中文翻译：

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基于投影的 port-Hamiltonian 系统保结构模型约简

在本文中，我们考虑了基于投影的多输入多输出端口哈密顿系统的结构保持模型约简。具体来说，我们证明了通过求解特定的 Sylvester 方程来构建投影矩阵的简化系统满足右（或左）切线插值条件并保留 port-Hamiltonian 结构；因此它仍然是被动的。基于切线插值，我们提出了两种用于端口-汉密尔顿系统的结构保持模型约简算法，并给出了几个数值例子来说明它们的有效性。