Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2008, Article ID 698043, 10 pages
http://dx.doi.org/10.1155/2008/698043
Research Article

Numerical Stability Test of Neutral Delay Differential Equations

Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China

Received 24 October 2007; Revised 1 March 2008; Accepted 16 March 2008

Academic Editor: Jose Balthazar

Copyright © 2008 Z. H. Wang. 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. G. Stépán and Z. Szabó, “Impact induced internal fatigue cracks,” in Proceedings of the ASME Design Engineering Technical Conferences (DETC '99), Las Vegas, Nev, USA, September 1999.
  2. A. Bellen, N. Guglielmi, and A. E. Ruehli, “Methods for linear systems of circuit delay differential equations of neutral type,” IEEE Transactions on Circuits and Systems, vol. 46, no. 1, pp. 212–216, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. G. Balanov, N. B. Janson, P. V. E. McClintock, R. W. Tucker, and C. H. T. Wang, “Bifurcation analysis of a neutral delay differential equation modelling the torsional motion of a driven drill-string,” Chaos, Solitons and Fractals, vol. 15, no. 2, pp. 381–394, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. Z. N. Masoud, M. F. Daqaq, and N. A. Nayfeh, “Pendulation reduction on small ship-mounted telescopic cranes,” Journal of Vibration and Control, vol. 10, no. 8, pp. 1167–1179, 2004. View at Publisher · View at Google Scholar
  5. D. A. W. Barton, Dynamics and bifurcations of non-smooth delay equations, Ph.D. dissertation, University of Bristol, Bristol, UK, 2006.
  6. Z. N. Masoud and A. H. Nayfeh, “Sway reduction on container cranes using delayed feedback controller,” Nonlinear Dynamics, vol. 34, no. 3-4, pp. 347–358, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. N. Kyrychko, K. B. Blyuss, A. Gonzalez-Buelga, S. J. Hogan, and D. J. Wagg, “Real-time dynamic substructuring in a coupled oscillator-pendulum system,” Proceedings of the Royal Society of London A, vol. 462, no. 2068, pp. 1271–1294, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Y. N. Kyrychko, S. J. Hogan, A. Gonzalez-Buelga, and D. J. Wagg, “Modelling real-time dynamic substructuring using partial delay differential equations,” Proceedings of the Royal Society of London A, vol. 463, no. 2082, pp. 1509–1523, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendulation reduction of ship-mounted cranes,” Nonlinear Dynamics, vol. 35, no. 3, pp. 299–311, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Y. Kuang, Delay Differential Equation with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993. View at MathSciNet
  11. Y. X. Qin, Y. Q. Liu, L. Wang, and Z. X. Zhen, Stability of Motion of Dynamical Systems with Time Lag, Science Press, Beijing, China, 2nd edition, 1989.
  12. G. Stépán, Retarded Dynamical Systems: Stability and Characteristic Functions, vol. 210 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1989. View at Zentralblatt MATH · View at MathSciNet
  13. S.-I. Niculescu, Delay Effects on Stability. A Robust Control Approach, vol. 269 of Lecture Notes in Control and Information Sciences, Springer, London, UK, 2001. View at Zentralblatt MATH · View at MathSciNet
  14. H. Y. Hu and Z. H. Wang, Dynamics of Controlled Mechanical Systems with Delayed Feedback, Springer, Berlin, Germany, 2002. View at Zentralblatt MATH · View at MathSciNet
  15. J. M. Krodkiewski and T. Jintanawan, “Stability improvement of periodic vibration of multi-degree-of-freedom systems by means of time-delay control,” in Proceedings of the International Conference on Vibration, Noise and Structural Dynamics, vol. 1, pp. 340–351, Venice, Italy, April, 1999.
  16. Z. H. Wang and H. Y. Hu, “Calculation of the rightmost characteristic root of retarded time-delay systems via Lambert W function,” to appear in Journal of Sound and Vibration.
  17. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Advances in Computational Mathematics, vol. 5, no. 4, pp. 329–359, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. C. Hwang and Y.-C. Cheng, “A note on the use of the Lambert W function in the stability analysis of time-delay systems,” Automatica, vol. 41, no. 11, pp. 1979–1985, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H. Shinozaki and T. Mori, “Robust stability analysis of linear time-delay systems by Lambert W function: some extreme point results,” Automatica, vol. 42, no. 10, pp. 1791–1799, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. Y. Fu, A. W. Olbrot, and M. P. Polis, “Robust stability for time-delay systems: the edge theorem and graphical tests,” IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 813–820, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. Y. Fu, A. W. Olbrot, and M. P. Polis, “The edge theorem and graphical tests for robust stability of neutral time-delay systems,” Automatica, vol. 27, no. 4, pp. 739–741, 1991. View at Google Scholar · View at MathSciNet
  22. W. Michiels and T. Vyhlídal, “An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type,” Automatica, vol. 41, no. 6, pp. 991–998, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. K. Engelborghs, T. Luzyanina, and G. Samaey, “DDE-BIFTOOL v2.0: a Matlab package for the computation analysis of delay differential equations,” Tech. Rep. TW220, Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium, 2001. View at Google Scholar