Model reduction of descriptor systems using frequency limited Gramians

Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, some applications require approximation over a certain band of frequency than whole frequency range. Different model reduction techniques are available for descriptor systems. However, for limited frequency interval, no such work exists in the literature. A frequency limited balanced truncation method for general descriptor systems is proposed. The method is an extension of truncated balanced realization method for the general descriptor system. The proposed technique generalizes the results of Gawronski and Juang technique for large-scale descriptor systems using frequency interval Gramians. Simple algorithms are also given for preserving the stability of reduced-order models. The work also extends Poor Man׳s truncated balanced realization technique to include frequency limited Gramians for descriptor systems. Practical numerical examples are incorporated to show the successful application of the proposed method in the desired frequency range.