Deepak Kumar and Shyam Krishna Nagar


  1. [1] K. Glover, All optimal Hankel norm approximation of linearmultivariable systems and their L∞ error bounds, InternationalJournal of Control, 39, 1984, 1115–1193.
  2. [2] S. Kung, A new identification and model reduction algorithmvia singular value decompositions, Proc. 12th Asilomar Con &Circuits, Syst., Comput., Pacific Grove, CA, 1978, 705–714.
  3. [3] B.C. Moore, Principal component analysis in linear systems:controllability, observability and model reduction, IEEE Trans-actions on Automatic Control, 26, 1981, 17–32.
  4. [4] V.M. Adamjan, D. Arov, and M.G. Krein, Analytic propertiesof Schmidt pairs for a Hankel operator and the generalizedSchur-Takagi problem, Math. Sbornik, 15(1), 1971, 31–73.
  5. [5] S. Kung and W.D. Lin, Optimal Hankel-Norm model reductions: multivariable systems, IEEE Transactions on Automatic Control, 26, 1981, 832–852.
  6. [6] L.M. Silverman and M. Bettayeb, Optimal approximation oflinear systems, Proc. Joint Automatic Control Conference, SanFrancisco, CA, 1980.
  7. [7] M. Bettayeb, L.M. Silverman, and M.G. Safonov, Optimal approximation of continuous-time systems, Proc CDC, Albu-querque, New Mexico, 1980.
  8. [8] S.Y. Kung and Y.V. Genin, A two-variable approach to themodel reduction problem with Hankel norm criterion, IEEETransactions on Circuits and Systems, 28, 1981, 912–924.
  9. [9] J.A. Ball and A.C.M. Ran, Hankel norm approximation of arational matrix function in terms of its realization, in C.L.Byrnes and A. Lindquist (eds), Modelling, identification androbust control (North-Holland: Amsterdam etc., 1986), 285–296.
  10. [10] J.A. Ball and A.C.M. Ran, Optimal Hankel norm model reductions and Wiener-Hopf factorization I: the canonical case,SIAM Journal of Control and Optimization, 25, 1987, 362–382.
  11. [11] M.G. Safonov, R.Y. Chiang, and D.J.N. Limebeer, OptimalHankel model reduction for nonminimal systems, IEEE Trans-actions on Automatic Control, 35, 1990, 496–502.
  12. [12] P. Benner, E.S. Quintana-Ort’I, and G. Quintana-Ort’, Com-puting optimal Hankel norm approximations of large scale systems, 43rd IEEE Conf. on Decision and Control, Bahamas,2004, 3078–3083.
  13. [13] M. Dehghani and M.J. Yazdanpanah, Model reduction basedon the frequency weighted Hankel norm using genetic algorithmand its application to power systems, Proc. IEEE Conf. onControl Applications, 2005, 245–250.
  14. [14] L. Chai, J. Zhang, C. Zhang, and E. Mosca, Hankel normapproximation of IIR by FIR models: a constructive method,IEEE Transactions on Circuits and Systems-I: Regular Papers,55(2), 2008, 586–598.
  15. [15] M. Ogura and Y. Yamamoto, Hankel norm computation forpseudorational transfer functions, Joint 48th IEEE Conf. onDecision and Control and 28th Chinese Control Conference,Shanghai, China, 2009, 5502–5507.
  16. [16] T. Fernandez, S.M. Djouadi, and J. Foster, Empirical Hankelnorm model reduction with application to a prototype nonlinearconvective flow, American Control Conference, Baltimore, MD,2010, 3771–3776.
  17. [17] D. Kumar, J.P. Tiwari, and S.K. Nagar, Reduction of unstable discrete time systems by Hankel norm approximation, International Journal of Engineering Science and Technology, 3(4), 2011, 2825–2831.
  18. [18] M.G. Safonov and G. Chiang, A Schur method for balancedtruncation Model reduction, IEEE Transactions on AutomaticControl, 34(7), 1989, 729–733.
  19. [19] S.K. Singh, S.K. Nagar, and J. Pal, Balanced realized reduced model of a non-minimal system with DC gain preservation,IEEE Conf. on Industrial Technology, IIT Bombay, 2006,1522–1527.
  20. [20] G.J. Lastman, N.K. Sinha, and P. Rozsa, On the selectionof the states to be retained in the reduced order model, IEEProceedings, 131, 1984, 15–22.

Important Links:

Go Back