Hankel-norm approximation is a model reduction method for linear time-invariant systems, which provides the best approximation in the Hankel semi-norm. In this paper, the computation of the optimal Hankel-norm approximation is generalized to the case of linear time-invariant continuous-time descriptor systems. A new algebraic characterization of all-pass descriptor systems is developed and used to construct an efficient algorithm by refining the generalized balanced truncation square root method. For a wide practical usage, adaptations of the introduced algorithm towards stable computations and sparse systems are suggested, as well as an approach for a projection-free algorithm. To show the approximation behavior of the introduced method, numerical examples are presented.

中文翻译：

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大规模描述符系统的Hankel范数逼近

Hankel范数逼近是线性时不变系统的模型归约方法，它在Hankel半范数中提供了最佳近似。在本文中，最优汉克尔范数逼近的计算被推广到线性时不变连续时间描述符系统的情况。提出了一种全通描述符系统的新代数表征方法，并通过细化广义平衡截断平方根方法来构造一种有效的算法。对于广泛的实际应用，建议将引入的算法适应稳定的计算和稀疏系统，以及一种无投影算法的方法。为了显示所引入方法的近似行为，给出了数值示例。