基于插值框架的传递函数主导极点的大规模估计
Large-Scale Estimation of Dominant Poles of a Transfer Function by an Interpolatory Framework
摘要：
我们主要研究广义系统的传递函数的主导极点。传递函数通常在主极点的虚部处和附近表现出大的范数。因此，主导极点提供了关于虚轴上的点的信息，在虚轴上达到系统的${\mathcal L}_\infty$范数，并且它们有时对于获得粗略的降阶模型也是有用的。对于一个大规模的广义系统，我们引入一个子空间框架来估计指定数量的主导极点。在每次迭代中，大系统被投影到一个小系统中，小系统的主导极点可以很容易地计算。然后扩展投影空间，使子空间扩展后的投影系统在计算出的主导极点处插值大系统。我们证明了至少二次收敛的框架的结果，并提供数值结果证实了这一点。在真实的基准示例上，所提出的框架似乎比SAMDP [IEEE Trans. Power Syst.21，1471-1483，2006]更可靠，SAMDP是由于Rommes和Martins用于估计主导极点的广泛使用的算法之一。
英文摘要：
We focus on the dominant poles of the transfer function of a descriptor system. The transfer function typically exhibits large norm at and near the imaginary parts of the dominant poles. Consequently, the dominant poles provide information about the points on the imaginary axis where the ${\mathcal L}_\infty$ norm of the system is attained, and they are also sometimes useful to obtain crude reduced-order models. For a large-scale descriptor system, we introduce a subspace framework to estimate a prescribed number of dominant poles. At every iteration, the large-scale system is projected into a small system, whose dominant poles can be computed at ease. Then the projection spaces are expanded so that the projected system after subspace expansion interpolates the large-scale system at the computed dominant poles. We prove an at-least-quadratic-convergence result for the framework, and provide numerical results confirming this. On real benchmark examples, the proposed framework appears to be more reliable than SAMDP [IEEE Trans. Power Syst. 21, 1471-1483, 2006], one of the widely used algorithms due to Rommes and Martins for the estimation of the dominant poles.
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