Model reduction for descriptor systems

Two SVD-based techniques to construct different types of lower degree approximants of a singular system are presented. Such techniques enable to preserve the key properties of the original system, such as stability, and give a quantization of approximation error. The first technique consists in reducing only the proper part of the descriptor system, while the second allows to reduce at once the proper and the improper parts of the system. The numerical results reveal the capabilities of the proposed techniques.