Extracting second-order structures from single-input state-space models: Application to model order reduction

Antoulas, A.C. (2005). Approximation of Large-Scale Dynamical Systems, Advances in Design and Control, SIAM, Philadelphia, PA.10.1137/1.9780898718713Search in Google Scholar

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. 75-94.10.1007/978-3-540-78841-6_4Search in Google Scholar

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.Search in Google Scholar

Chahlaoui, Y., Lemonnier, D., Vandendorpe, A. and Dooren, P. V. (2006). Second-order balanced truncation, Linear Algebra and Its Applications 415(2-3): 373-384.10.1016/j.laa.2004.03.032Search in Google Scholar

Dorf, R.C. and Bishop, R.H. (2008). Modern Control Systems, 11th Edn., Prentice Hall, Upper Saddle River, NJ.Search in Google Scholar

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.10.1115/IMECE2007-42031Search in Google Scholar

Fortuna, L., Nunnari, G. and Gallo, A. (1992). Model Order Reduction Techniques with Applications in Electrical Engineering, Springer-Verlag, Berlin/Heidelberg.10.1007/978-1-4471-3198-4Search in Google Scholar

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.Search in Google Scholar

Friswell, M.I. (1999). Extracting second-order system from state-space representations, American Institute of Aeronautics and Astronautics Journal 37(1): 132-135.10.2514/2.679Search in Google Scholar

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): 311-323.10.1006/jsvi.1995.0451Search in Google Scholar

Glover, K. (1984). All optimal Hankel-norm approximation of linear multivariable systems and their L∞-error bounds, International Journal of Control 39(6): 1115-1193.10.1080/00207178408933239Search in Google Scholar

Gohberg, I., Lancaster, P. and Rodman, L. (1982). Matrix Polynomials, Academic Press, New York, NY.Search in Google Scholar

Gugercin, S. (2004). A survey off-road model reduction by balanced truncation and some new results, International Journal of Control 77(8): 748-766.10.1080/00207170410001713448Search in Google Scholar

Guyan, R. (1964). Reduction of stiffness and mass matrices, American Institute of Aeronautics and Astronautics Journal 3(2): 380.10.2514/3.2874Search in Google Scholar

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): 1147-1149.10.1243/09544062JMES341Search in Google Scholar

Hughes, P. and Skelton, R. (1980). Controllability and observability of linear matrix-second-order systems, Journal of Applied Mechanics 47(2): 415-420.10.1115/1.3153679Search in Google Scholar

Koutsovasilis, P. and Beitelschmidt, M. (2008). Comparison of model reduction techniques for large mechanical systems, Multibody System Dynamics 20(2): 111-128.10.1007/s11044-008-9116-4Search in Google Scholar

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.Search in Google Scholar

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. 323-332.10.1007/11558958_38Search in Google Scholar

Meyer, D.G. and Sirnivasan, S. (1996). Balancing and model reduction for second-order form linear systems, IEEE Transactions on Automatic Control 41(11): 1632-644.10.1109/9.544000Search in Google Scholar

Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control ac-26(1): 17-32.10.1109/TAC.1981.1102568Search in Google Scholar

Prells, U. and Lancaster, P. (2005). Isospectral vibrating systems. Part 2: Structure preserving transformation, Operator Theory 163: 275-298.Search in Google Scholar

Reis, T. and Stykel, T. (2007). Balanced truncation model reduction of second-order systems, Technical report, DFG Research Center Matheon, Berlin.Search in Google Scholar

Salimbahrami, S.B. (2005). Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technical University of Munchen, Munchen.Search in Google Scholar

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. 3-32.10.1007/978-3-540-78841-6_1Search in Google Scholar

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.Search in Google Scholar

Stykel, T. (2006). Balanced truncation model reduction of second-order systems, Proceedings of 5th MATHMOD, Vienna, Austria.Search in Google Scholar

Tisseur, F. and Meerbergen, K. (2001). The quadratic eigenvalue problem, Society for Industrial and Applied Mathematics Review 43(2): 235-286.10.1137/S0036144500381988Search in Google Scholar

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): 942-946.10.1109/TCSII.2008.925655Search in Google Scholar