A greedy rational Krylov method for ℋ2-pseudooptimal model order reduction with preservation of stability

We present a new approach to the problem of finding suitable expansion points in Krylov subspace methods for the model reduction of LTI systems. Using a factorized formulation of the resulting error model, we can efficiently apply a greedy algorithm and perform multiple reduction steps instead of looking for all shifts at once. An expedient globally convergent optimization algorithm delivers locally ℋ₂-optimal two-dimensional ROMs in each step. The overall ROM, whose error decreases monotonically, is ℋ₂-pseudooptimal and guaranteed to be stable; its order can be chosen on-the-fly. Ready-to-run Matlab demo code is provided in the Appendix.