An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems

✍ Scribed by Serkan Gugercin

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 292 KB
• Volume: 428
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.10.041

✦ Synopsis

In this paper, we propose a model reduction algorithm for approximation of large-scale linear timeinvariant dynamical systems. The method is a two-sided projection combining features of the singular value decomposition (SVD)-based and the Krylov-based model reduction techniques. While the SVD-side of the projection depends on the observability gramian, the Krylov-side is obtained via iterative rational Krylov steps. The reduced model is asymptotically stable, matches certain moments and solves a restricted H 2 minimization problem. We present modifications to the proposed approach for employing low-rank gramians in the reduction step and also for reducing discrete-time systems. Several numerical examples from various disciplines verify the effectiveness of the proposed approach. It performs significantly better than the q-cover [A. Yousouff, R.E. Skelton, Covariance equivalent realizations with applications to model reduction of large-scale systems, in: