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Passivity Preserving Frequency Weighted Model Order Reduction Technique

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Abstract

A new passivity preserving frequency weighted balanced model order reduction technique is proposed. The proposed technique preserves passivity (and stability) of reduced-order models for the case when both input and output weightings are included. Numerical examples are presented to show the usefulness and effectiveness of the proposed technique.

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References

  1. D.F. Enns, Model reduction with balanced realizations: an error bound and a frequency weighted generalization, in Proceedings of Conference on Decision and Control (1984), pp. 127–132

  2. A. Ghafoor, M. Imran, Hierarchical balancing approach for frequency-weighted model reduction. IET Electron. Lett. 51(10), 763–765 (2015)

    Article  Google Scholar 

  3. A. Ghafoor, V. Sreeram, A survey/review of frequency-weighted balanced model reduction techniques. ASME J. Dyn. Syst. Meas. Control 130(6), 1–16 (2008)

    Article  Google Scholar 

  4. A. Ghafoor, V. Sreeram, Model reduction via limited frequency interval Gramians. IEEE Trans. Circuits Syst. I Regul. Pap. 55(9), 2806–2812 (2008)

    Article  MathSciNet  Google Scholar 

  5. P. Heydari, M. Pedram, Model order reduction using variational balanced truncation with spectral shaping. IEEE Trans. Circuits Syst. I Regul. Pap. 53(4), 879–891 (2006)

    Article  MathSciNet  Google Scholar 

  6. M. Imran, A. Ghafoor, Stability preserving model order reduction technique using frequency limited Gramians for discrete time systems. IEEE Trans. Circuits Syst. II Exp. Briefs 61(9), 716–720 (2014)

    Article  Google Scholar 

  7. M. Imran, A. Ghafoor, Limited frequency Gramians based model reduction technique and error bound. Circuits Syst. Signal Process. 34(11), 3505–3519 (2015)

    Article  MATH  Google Scholar 

  8. M. Imran, A. Ghafoor, V. Sreeram, A frequency weighted model order reduction technique and error bounds. Automatica 50(12), 3304–3309 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. X. Li, H. Gao, Robust finite frequency \(H_\infty \) filtering for uncertain 2-D systems: the FM model case. Automatica 49(8), 2446–2452 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. X. Li, S. Yin, H. Gao, Passivity preserving model reduction with finite frequency \(H_\infty \) approximation performance. Automatica 50(9), 2294–2303 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. C.A. Lin, T.Y. Chiu, Model reduction via frequency weighted balanced realization. Control Theory Adv. Technol. 8, 341–451 (1992)

    MathSciNet  Google Scholar 

  12. W.M. Muda, Frequency weighted model order reduction techniques. Ph.D. Dissertation. University of Western Australia (2012)

  13. W.M. Muda, V. Sreeram, H.H.C. Lu, Passivity-preserving frequency weighted model order reduction techniques for general large-scale RLC sytems, in IEEE Conference on Control Automation Robotics and Vision (2010), pp. 1310–1315

  14. W.M. Muda, V. Sreeram, M.B. Ha, A. Ghafoor, Comments on: Model order reduction using variational balanced truncation with spectral shaping. IEEE Trans. Circuits Syst. I Regul. Pap. 62(1), 333–335 (2015)

    Article  Google Scholar 

  15. A. Odabasioglu, M. Celik, L. Pileggi, PRIMA: passive reduced-order interconnect macromodeling algorithm. IEEE Trans. Comput. Aided Des. Int. Circuits Syst. 17(8), 645–654 (1998)

    Article  Google Scholar 

  16. J.R. Phillips, L. Daniel, L.M. Silveira, Guaranteed passive balancing transformations for model order reduction. IEEE Trans. Comput. Aided Des. Int. Circuits Syst. 22(8), 1027–1041 (2003)

    Article  Google Scholar 

  17. N. Sadegh, J.D. Finney, B.S. Heck, An explicit method for computing the positive real lemma matrices. Int. J. Robust Nonlinear Control 7(12), 1057–1069 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. K. Unneland, P.V. Dooren, O. Egeland, A novel scheme for positive real balanced truncation, in Proceedings of American Control Conference (2007), pp. 947–952

  19. A. Varga, B.D.O. Anderson, Accuracy-enhancing methods for balancing-related frequency-weighted model and controller reduction. Automatica 39(5), 919–927 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. G. Wang, V. Sreeram, W.Q. Liu, A new frequency weighted balanced truncation method and an error bound. IEEE Trans. Autom. Control 44(9), 1734–1737 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  21. B. Yan, S.D. Tan, P. Liu, B. McGaughy, Passive interconnect macromodeling via balanced truncation of linear systems in descriptor form, in Proceedings of Asia and South Pacific Design Automatic Conference (2007), pp. 355–360

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Authors and Affiliations

  1. Department of Information Security, Military College of Signals, National University of Science and Technology (NUST), Islamabad, Pakistan

    Abdul Ghafoor

  2. Department of Electrical Engineering, Military College of Signals, National University of Science and Technology (NUST), Islamabad, Pakistan

    Muhammad Imran

Authors
  1. Abdul Ghafoor
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  2. Muhammad Imran
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Correspondence to Abdul Ghafoor.

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Ghafoor, A., Imran, M. Passivity Preserving Frequency Weighted Model Order Reduction Technique. Circuits Syst Signal Process 36, 4388–4400 (2017). https://doi.org/10.1007/s00034-017-0540-7

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  • DOI: https://doi.org/10.1007/s00034-017-0540-7

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