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Mathematical and Computer Modelling of Dynamical Systems
Methods, Tools and Applications in Engineering and Related Sciences
Volume 20, 2014 - Issue 4
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Original Articles

Structure-preserving approximation of distributed-parameter second-order systems using Krylov subspaces

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Pages 395-413 | Received 05 Jun 2013, Accepted 07 Aug 2013, Published online: 06 Sep 2013

References

  • D. Meyer and S. Srinivasan, Balancing and model reduction for second-order form linear systems, IEEE Trans. Autom. Control 41 (1996), pp. 1632–1644.
  • Y. Chahlaoui, D. Lemonnier, K. Meerbergen, A. Vandendorpe, and P.V. Dooren, Model Reduction of Second-order Systems, Proc. Int. Symp. on Mathematical Theory of Networks and Systems, University of Notre Dame, USA, 2002.
  • T. Reis and T. Stykel, Balanced truncation model reduction of second-order systems, Math. Comp. Modelling Dyn. Sys. 14 (2008), pp. 391–406.
  • P. Benner, P. Kürschner, and J. Saak, An Improved Numerical Method for Balanced Truncation for Symmetric Second-Order Systems, Max Planck Institute, Magdeburg, preprints MPIMD/12-20. 2012.
  • A.C. Antoulas, Approximation of Large-scale Dynamical Systems, SIAM Press, Philadelphia, PA, 2005.
  • R.W. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica 12 (2003), pp. 267–319.
  • E.J. Grimme, Krylov projection methods for model reduction, Ph.D. Thesis, ECE Department, University of Illinois, Urbana-Champaign, 1997.
  • B. Salimbahrami and B. Lohmann, Order reduction of large scale second-order systems using Krylov subspace methods, Lin. Alg. Appl. 415 (2006), pp. 385–405.
  • R. Eid, B. Salimbahrami, and B. Lohmann, Parametric order reduction of proportionally damped second-order systems, Technical Reports on Automatic Control 1 (2006), Available at: www.rt.mw.tum.de .
  • Z. Bai and Y. Su, Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method, SIAM J. Sci. Comput. 26 (2005), pp. 1692–1709.
  • C. Beattie and S. Gugercin, Krylov-based model reduction of second-order systems with proportional damping, Proc. CDC, Seville, Spain (2005), pp. 2278–2283.
  • C. Beattie and S. Gugercin, Interpolatory projection methods for structure-preserving model reduction, Syst. Control Lett. 58 (2009), pp. 225–232.
  • T. Reis and W. Wollner, Finite-rank ADI iteration for operator Lyapunov equations, Hamburger Beiträge zur Angewandten Mathematik, Nr. 2012–09, 2012.
  • C. Harkort and J. Deutscher, Krylov subspace methods for linear infinite-dimensional systems, IEEE Trans. Autom. Control 56 (2011), pp. 441–447.
  • B. Salimbahrami, Structure-preserving order reduction of large scale second-order models, Doctoral thesis, Lehrstuhl für Regelungstechnik, Universität München, Germany, 2005.
  • C. Fletcher, Computational Galerkin Methods, Springer-Verlag, New York, 1984.
  • R.F. Curtain and H.J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Springer-Verlag, New York, 1995.
  • Z.H. Luo, B.Z. Guo, and Ö. Morgül, Stability and Stabilization of Infinite Dimensional Systems with Applications, Springer-Verlag, London, 1999.
  • F. Huang, On the mathematical model for linear elastic systems with analytic damping, SIAM J. Control Optim. 26 (1988), pp. 714–724.
  • R. Griniv and A. Shkalikov, Exponential stability of semigroups related to operator models in mechanics, Math. Notes 73 (2003), pp. 618–624.
  • E.E. Zajac, Comments on “Stability of damped mechanical systems” and a further extension, AIAA J. 3 (1965), pp. 1749–1750.
  • T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1995.

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