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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 796143, 13 pages
http://dx.doi.org/10.1155/2010/796143
Research Article

The Robust Pole Assignment Problem for Second-Order Systems

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 13 April 2010; Accepted 12 October 2010

Academic Editor: J. Rodellar

Copyright © 2010 Hao Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S.-F. Xu, An Introduction to Inverse Algebraic Eigenvalue Problems, Peking University Press, Beijing, China, 1998. View at Zentralblatt MATH
  2. S. Q. Zhou and H. Dai, The Algebraic Inverse Eigenvalue Problem, Henan Science and Technology Press, Zhengzhou, China, 1991.
  3. A. J. Laub and W. F. Arnold, “Controllability and observability criteria for multivariable linear second-order models,” IEEE Transactions on Automatic Control, vol. 29, no. 2, pp. 163–165, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. E. K. Chu and B. N. Datta, “Numerically robust pole assignment for second-order systems,” International Journal of Control, vol. 64, no. 6, pp. 1113–1127, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. N. K. Nichols and J. Kautsky, “Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case,” SIAM Journal on Matrix Analysis and Applications, vol. 23, no. 1, pp. 77–102, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. B. N. Datta and D. R. Sarkissian, “Theory and computations of some inverse eigenvalue problems for the quadratic pencil,” in Structured Matrices in Mathematics, Computer Science, and Engineering, I (Boulder, CO, 1999), vol. 280 of Contemp. Math., pp. 221–240, Amer. Math. Soc., Providence, RI, USA, 2001. View at Google Scholar · View at Zentralblatt MATH
  7. J. Qian, Numerical methods for pole assignment problem, Ph.D. thesis, Peking University, Beijing, China, 2004.
  8. J. Qian and S. Xu, “Robust partial eigenvalue assignment problem for the second-order system,” Journal of Sound and Vibration, vol. 282, no. 3-5, pp. 937–948, 2005. View at Publisher · View at Google Scholar
  9. Z.-J. Bai, B. N. Datta, and J. Wang, “Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: a new optimization approach,” Mechanical Systems and Signal Processing, vol. 24, pp. 766–783, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. J. G. Sun, “On numerical methods for robust pole assignment in control system design,” Journal of Computational Mathematics, vol. 5, no. 2, pp. 119–134, 1987. View at Google Scholar · View at Zentralblatt MATH
  11. J. G. Sun, “On numerical methods for robust pole assignment in control system design. II,” Journal of Computational Mathematics, vol. 5, no. 4, pp. 352–363, 1987. View at Google Scholar · View at Zentralblatt MATH
  12. D. G. Luenberger, Introduction to Linear and Nonlinear Programming, Addison-Wesley, Reading, Mass, USA, 1973.
  13. J. G. Sun, “An algorithm for the solution of multiparameter eigenvalue problems. I,” Mathematica Numerica Sinica, vol. 8, no. 2, pp. 137–149, 1986. View at Google Scholar
  14. P. Horst, “Relations among m sets of measures,” Psychometrika, vol. 26, pp. 129–149, 1961. View at Google Scholar · View at Zentralblatt MATH
  15. J. Kautsky, N. K. Nichols, and P. Van Dooren, “Robust pole assignment in linear state feedback,” International Journal of Control, vol. 41, no. 5, pp. 1129–1155, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. B. N. Datta, S. Elhay, Y. M. Ram, and D. R. Sarkissian, “Partial eigenstructure assignment for the quadratic pencil,” Journal of Sound and Vibration, vol. 230, no. 1, pp. 101–110, 2000. View at Publisher · View at Google Scholar