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Journal of Mathematics
Volume 2013, Article ID 365909, 6 pages
http://dx.doi.org/10.1155/2013/365909
Research Article

A Unified Software Framework for Empirical Gramians

Institute for Computational and Applied Mathematics, University of Münster, Einsteinstraße 62, 48149 Münster, Germany

Received 11 July 2013; Accepted 2 August 2013

Academic Editor: Beny Neta

Copyright © 2013 Christian Himpe and Mario Ohlberger. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. C. Moore, “Principal component analysis in linear systems: controllability, observability, and model reduction,” IEEE Transactions on Automatic Control, vol. 26, no. 1, pp. 17–32, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Lall, J. E. Marsden, and S. Glavaski, “Empirical model reduction of controlled nonlinear systems,” in Proceedings of the International Federation of Automatic Control World Congress (IFAC '99), pp. 473–478, 1999.
  3. J. Hahn and T. F. Edgar, “Balancing approach to minimal realization and model reduction of stable nonlinear systems,” Industrial and Engineering Chemistry Research, vol. 41, no. 9, pp. 2204–2212, 2002. View at Google Scholar · View at Scopus
  4. A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, Advances in Design and Control, SIAM, Philadelphia, Pa, USA, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  5. S. Streif, R. Findeisen, and E. Bullinger, “Relating cross gramians and sensitivity analysis in systems biology,” in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS '06), pp. 437–442, 2006.
  6. C. Himpe and M. Ohlberger, “Cross-Gramian based combined state and parameter reduction,” http://arxiv.org/abs/1302.0634. View at Google Scholar
  7. C. Sun and J. Hahn, “Parameter reduction for stable dynamical systems based on Hankel singular values and sensitivity analysis,” Chemical Engineering Science, vol. 61, no. 16, pp. 5393–5403, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. D. Geffen, R. Findeisen, M. Schliemann, F. Allgöwer, and M. Guay, “Observability based parameter identifiability for biochemical reaction networks,” in Proceedings of the American Control Conference (ACC '08), pp. 2130–2135, June 2008. View at Publisher · View at Google Scholar · View at Scopus