Interpolatory model reduction techniques for linear second-order descriptor systems

Standard interpolatory subspaces for model reduction of linear descriptor systems may produce unbounded ℋ₂ or ℋ_∞ error. In this paper we investigate this issue and discuss modified interpolatory subspaces based on spectral projectors that ensure bounded errors. In the special case of index-3 descriptor systems, we show how to transform the system to an equivalent system that enables the use of standard interpolatory subspaces for model reduction with bounded errors, but without the explicit computation of spectral projectors. The approach can also be used to update interpolation points in the framework of ℋ₂-norm approximation, thus extending the Iterative Rational Krylov Algorithm (IRKA) to index-3 descriptor systems. Also it is shown that the index-3 structure of the actual system can be preserved in the reduced order interpolating approximation.