References
- Antoulas, A.C. (2005). Approximation of Large-Scale Dynamical Systems, Advances in Design and Control, SIAM, Philadelphia, PA.
- Bai, Z., Li, R.-C. and Su, Y. (2008). A unified Krylov projection framework for structure-preserving model reduction, in W.H. Schilders, H.A. van der Vorst and J. Rommres (Eds.) Model Order Reduction: Theory, Research Aspects and Applications, Springer, Berlin/Heidelberg, pp. 75-94.
- Chahlaoui, Y., Lemonnier, D., Meerbergen, K., Vandendorpe, A. and Dooren, P.V. (2002). Model reduction of second order systems, Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems of Notre Dame, South Bend, IN, USA.
- Chahlaoui, Y., Lemonnier, D., Vandendorpe, A. and Dooren, P. V. (2006). Second-order balanced truncation, Linear Algebra and Its Applications 415(2-3): 373-384.
- Dorf, R.C. and Bishop, R.H. (2008). Modern Control Systems, 11th Edn., Prentice Hall, Upper Saddle River, NJ.
- Ersal, T., Fathy, T.H., Louca, L., Rideout, D. and Stein, J. (2007). A review of proper modeling techniques, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Seattle, WA, USA.
- Fortuna, L., Nunnari, G. and Gallo, A. (1992). Model Order Reduction Techniques with Applications in Electrical Engineering, Springer-Verlag, Berlin/Heidelberg.
- Freund, R.W. (2005). PadéeA-type model reduction of second-order and higher-order linear dynamical systems, in V.M. P. Benner and D. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Berlin/Heidelberg, pp. 191-223.
- Friswell, M.I. (1999). Extracting second-order system from state-space representations, American Institute of Aeronautics and Astronautics Journal 37(1): 132-135.
- Friswell, M.I., Garvey, S.D. and Penny, J.E.T. (1995). Model reduction using dynamic and iterated IRS techniques, Journal of Sound and Vibration 186(2): 311-323.
- Glover, K. (1984). All optimal Hankel-norm approximation of linear multivariable systems and their L∞-error bounds, International Journal of Control 39(6): 1115-1193.
- Gohberg, I., Lancaster, P. and Rodman, L. (1982). Matrix Polynomials, Academic Press, New York, NY.
- Gugercin, S. (2004). A survey off-road model reduction by balanced truncation and some new results, International Journal of Control 77(8): 748-766.
- Guyan, R. (1964). Reduction of stiffness and mass matrices, American Institute of Aeronautics and Astronautics Journal 3(2): 380.
- Houlston, P.R. (2006). Extracting second order system matrices from state space system, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220(8): 1147-1149.
- Hughes, P. and Skelton, R. (1980). Controllability and observability of linear matrix-second-order systems, Journal of Applied Mechanics 47(2): 415-420.
- Koutsovasilis, P. and Beitelschmidt, M. (2008). Comparison of model reduction techniques for large mechanical systems, Multibody System Dynamics 20(2): 111-128.
- Li, J.-R. and White, J. (2001). Reduction of large circuit models via low rank approximate gramians, International Journal of Applied Mathematics and Computer Science 11(5): 1151-1171.
- Li, R.-C. and Bai, Z. (2006). Structure-preserving model reduction, in J. Dongarra, K. Madsen and J. WaésAniewski (Eds.) PARA 2004, Lecture Notes in Computer Science, Vol. 3732, Springer-Verlag, Berlin/Heidelberg, pp. 323-332.
- Meyer, D.G. and Sirnivasan, S. (1996). Balancing and model reduction for second-order form linear systems, IEEE Transactions on Automatic Control 41(11): 1632-644.
- Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control ac-26(1): 17-32.
- Prells, U. and Lancaster, P. (2005). Isospectral vibrating systems. Part 2: Structure preserving transformation, Operator Theory 163: 275-298.
- Reis, T. and Stykel, T. (2007). Balanced truncation model reduction of second-order systems, Technical report, DFG Research Center Matheon, Berlin.
- Salimbahrami, S.B. (2005). Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technical University of Munchen, Munchen.
- Schilders, W.H.A. (2008). Introduction to model order reduction, in W.H. Schilders, H.A. van der Vorst and J. Ronnres (Eds.) Model Order Reduction: Theory, Research Aspects and Applications, Springer, Berlin/Heidelberg, pp. 3-32.
- Sorensen, D. and Antoulas, A. (2004). Gramians of structured systems and an error bound for structure-preserving model reduction, in V.M.P. Benner and D. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Heidelberg/Berlin, pp. 117-130.
- Stykel, T. (2006). Balanced truncation model reduction of second-order systems, Proceedings of 5th MATHMOD, Vienna, Austria.
- Tisseur, F. and Meerbergen, K. (2001). The quadratic eigenvalue problem, Society for Industrial and Applied Mathematics Review 43(2): 235-286.
- Yan, B., Tan, S.-D. and Gaughy, B.M. (2008). Second-order balanced truncation for passive order reduction of RLCK circuits, IEEE Transactions on Circuits and Systems II 55(9): 942-946.