  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.
