We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to construct this optimal solution. We also consider the problem of finding the nearest passive system to a given non-passive one and provide a simple but suboptimal solution.

中文翻译：

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哈密​​尔顿港系统的最优鲁棒性

我们构建了代表无源系统的给定有理传递函数的最优鲁棒哈密尔顿端口实现。我们证明了具有最大被动半径的实现是归一化的哈密顿端口。它的计算与定义传递函数的被动性的线性矩阵不等式的特定解相关，我们提供了一种算法来构建此最优解。我们还考虑了找到最接近给定非无源系统的无源系统的问题，并提供了一个简单但次优的解决方案。