Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 268684, 16 pages
http://dx.doi.org/10.1155/2013/268684
Research Article

Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case

1College of Automation, Chongqing University, Chongqing 400044, China
2Department of Mathematics, Guiyang University, Guiyang 550005, China
3Key Laboratory of Dependable Service Computing in Cyber Physical Society Ministry of Education, Chongqing University, Chongqing 400044, China
4Department of Electric and Electronic Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, China

Received 17 July 2013; Revised 11 October 2013; Accepted 21 October 2013

Academic Editor: Baocang Ding

Copyright © 2013 Cheng Zeng et al. 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. K. J. Åström, P. Hagander, and J. Sternby, “Zeros of sampled systems,” Automatica, vol. 20, no. 1, pp. 31–38, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. T. Hagiwara and M. Araki, “Properties of limiting zeros of sampled systems,” Transactions of the Institute of Electrical Engineers of Japan, vol. 110-C, no. 4, pp. 235–244, 1990 (Japanese). View at Google Scholar
  3. T. Hagiwara, “Analytic study on the intrinsic zeros of sampled-data systems,” IEEE Transactions on Automatic Control, vol. 41, no. 2, pp. 261–263, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. Hagiwara, T. Yuasa, and M. Araki, “Stability of the limiting zeros of sampled-data systems with zero- and first-order holds,” International Journal of Control, vol. 58, no. 6, pp. 1325–1346, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. R. Weller, W. Moran, B. Ninness, and A. D. Pollington, “Sampling zeros and the Euler-Frobenius polynomials,” IEEE Transactions on Automatic Control, vol. 46, no. 2, pp. 340–343, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. J. Błachuta, “On zeros of pulse transfer functions,” IEEE Transactions on Automatic Control, vol. 44, no. 6, pp. C1229–C1234, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. Hayakawa, S. Hosoe, and M. Ito, “On the limiting zeros of sampled multivariable systems,” Systems & Control Letters, vol. 2, no. 5, pp. 292–300, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. R. Weller, “Limiting zeros of decouplable MIMO systems,” IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 129–134, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Ishitobi, “A stability condition of zeros of sampled multivariable systems,” IEEE Transactions on Automatic Control, vol. 45, no. 2, pp. 295–299, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Liang, M. Ishitobi, W. R. Shi, and X. D. Xian, “On stability of the limiting zeros of discrete-time MIMO systems,” Acta Automatica Sinica, vol. 33, no. 4, pp. 439–441, 2007 (Chinese). View at Google Scholar · View at MathSciNet
  11. K. M. Passino and P. J. Antsaklis, “Inverse stable stampled low-pass systems,” International Journal of Control, vol. 47, no. 6, pp. 1905–1913, 1988. View at Google Scholar · View at Scopus
  12. M. Ishitobi, “Stability of zeros of sampled system with fractional order hold,” IEE Proceedings, vol. 143, no. 3, pp. 296–300, 1996. View at Publisher · View at Google Scholar
  13. R . Bàrcena, M . de la Sen, and I . Sagastabeitia, “Improving the stability properties of the zeros of sampled systems with fractional order hold,” IEE Proceedings, vol. 147, no. 4, pp. 456–464, 2000. View at Publisher · View at Google Scholar
  14. R. Bárcena, M. de la Sen, I. Sagastabeitia, and J. M. Collantes, “Discrete control for a computer hard disk by using a fractional order hold device,” IEE Proceedings, vol. 148, no. 2, pp. 117–124, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Liang, M. Ishitobi, and Q. Zhu, “Improvement of stability of zeros in discrete-time multivariable systems using fractional-order hold,” International Journal of Control, vol. 76, no. 17, pp. 1699–1711, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. Liang and M. Ishitobi, “The stability properties of the zeros of sampled models for time delay systems in fractional order hold case,” Dynamics of Continuous, Discrete & Impulsive Systems B, vol. 11, no. 3, pp. 299–312, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. J. Blachuta, “On fast sampling zeros of systems with fractional-order hold,” in Proceedings of the American Control Conference, vol. 4, pp. 3229–3230, Arlington, Va, USA, June 2001. View at Scopus
  18. M. Ishitobi, “Properties of zeros of a discrete-time system with fractional order hold,” in Proceedings of the 35th IEEE Conference on Decision and Control (CDC '96), pp. 4339–4344, Kobe, Japan, December 1996. View at Scopus
  19. A. Isidori, Nonlinear Control Systems: An Introduction, Springer, Berlin, Germany, 1995.
  20. H. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 2002.
  21. M. Ishitobi, T. Koga, M. Nishi, and S. Kunimatsu, “Asymptotic properties of zeros of sampled-data systems,” in Proceedings of the 49th IEEE Conference on Decision and Control (CDC '10), pp. 4952–4957, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Ishitobi and Q. Zhu, “Zeros of sampled systems with fractional order hold implemented by zero order hold,” in Proceedings of the 1997 IEEE International Conference on Intelligent Processing Systems (ICIPS '97), pp. 698–702, Beijing, China, October 1997. View at Scopus
  23. T. Hagiwara, T. Yuasa, and M. Araki, “Limiting properties of the zeros of sampled-data systems with zero- and firstorder holds,” in Proceedings of the 31th Conference on Decision and Control (CDC '92), pp. 1949–1954, Tuscon, Ariz, USA, 1992. View at Publisher · View at Google Scholar
  24. S. Liang, M. Ishitobi, T. Koga, and S. Kunimatsu, “On zeros of sampled-data system with relative degree two,” in Proceedings of the International Conference on Advanced Mechatronic Systems (ICAMechS '11), pp. 67–71, Zhengzhou, China, August 2011. View at Scopus
  25. M. de la Sen, R. Bárcena, and A. J. Garrido, “On the intrinsic limiting zeros as the sampling period tends to zero,” IEEE Transactions on Circuits and Systems I, vol. 48, no. 7, pp. 898–900, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet