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

 Access to full text

 Full (PDF)

1. Antoulas, A.C. (2005). Approximation of Large-Scale Dynamical Systems, Advances in Design and Control, SIAM, Philadelphia, PA. Zbl1112.93002
2. 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. Zbl1154.93010
3. 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. 
4. 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. Zbl1102.93008
5. Dorf, R.C. and Bishop, R.H. (2008). Modern Control Systems, 11th Edn., Prentice Hall, Upper Saddle River, NJ. Zbl0907.93001
6. 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. 
7. Fortuna, L., Nunnari, G. and Gallo, A. (1992). Model Order Reduction Techniques with Applications in Electrical Engineering, Springer-Verlag, Berlin/Heidelberg. 
8. Freund, R.W. (2005). Padé-type model reduction of secondorder 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. Zbl1079.65532
9. Friswell, M.I. (1999). Extracting second-order system from state-space representations, American Institute of Aeronautics and Astronautics Journal 37(1): 132-135. 
10. 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. Zbl1049.74725
11. Glover, K. (1984). All optimal Hankel-norm approximation of linear multivariable systems and their $L_{\infty }$-error bounds, International Journal of Control 39(6): 1115-1193. Zbl0543.93036
12. Gohberg, I., Lancaster, P. and Rodman, L. (1982). Matrix Polynomials, Academic Press, New York, NY. Zbl0482.15001
13. Gugercin, S. (2004). A survey off-road model reduction by balanced truncation and some new results, International Journal of Control 77(8): 748-766. Zbl1061.93022
14. Guyan, R. (1964). Reduction of stiffness and mass matrices, American Institute of Aeronautics and Astronautics Journal 3(2): 380. 
15. 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. 
16. Hughes, P. and Skelton, R. (1980). Controllability and observability of linear matrix-second-order systems, Journal of Applied Mechanics 47(2): 415-420. Zbl0441.73117
17. Koutsovasilis, P. and Beitelschmidt, M. (2008). Comparison of model reduction techniques for large mechanical systems, Multibody System Dynamics 20(2): 111-128. Zbl1332.70024
18. 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. Zbl0995.93027
19. Li, R.-C. and Bai, Z. (2006). Structure-preserving model reduction, in J. Dongarra, K. Madsen and J. Waśniewski (Eds.) PARA 2004, Lecture Notes in Computer Science, Vol. 3732, Springer-Verlag, Berlin/Heidelberg, pp. 323-332. 
20. 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. 
21. Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control ac-26(1): 17-32. Zbl0464.93022
22. Prells, U. and Lancaster, P. (2005). Isospectral vibrating systems. Part 2: Structure preserving transformation, Operator Theory 163: 275-298. Zbl1095.15017
23. Reis, T. and Stykel, T. (2007). Balanced truncation model reduction of second-order systems, Technical report, DFG Research Center Matheon, Berlin. Zbl1151.93010
24. Salimbahrami, S.B. (2005). Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technical University of Munchen, Munchen. 
25. 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. Zbl1154.93322
26. 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. 
27. Stykel, T. (2006). Balanced truncation model reduction of second-order systems, Proceedings of 5th MATHMOD, Vienna, Austria. Zbl1102.65075
28. Tisseur, F. and Meerbergen, K. (2001). The quadratic eigenvalue problem, Society for Industrial and Applied Mathematics Review 43(2): 235-286. Zbl0985.65028
29. 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.