Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 620546, 27 pages
doi:10.1155/2010/620546
Research Article

Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls

S. Alonso-Quesada and M. De la Sen

Department of Electricity and Electronics, Faculty of Science and Technology, University of Basque Country, Leioa 48940, Spain

Received 8 June 2009; Accepted 2 February 2010

Academic Editor: Francisco Solis

Copyright © 2010 S. Alonso-Quesada and M. De la Sen. 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. P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice-Hall, Englewood Cliffs, NJ, USA, 1996.
  2. S. Alonso-Quesada and M. De la Sen, “Robust adaptive control of discrete nominally stabilizable plants,” Applied Mathematics and Computation, vol. 150, no. 2, pp. 555–583, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. Alonso-Quesada and M. De la Sen, “Robust adaptive stabilizer for linear systems with imperfectly known point delays using a multi-estimation model,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B, vol. 15, no. 5, pp. 683–708, 2008. View at Zentralblatt MATH · View at MathSciNet
  4. M. De la Sen and A. Ibeas, “On the global asymptotic stability of switched linear time-varying systems with constant point delays,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 231710, 31 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. De la Sen and A. Ibeas, “Stability results of a class of hybrid systems under switched continuous-time and discrete-time control,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 315713, 28 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Ibeas, M. De la Sen, and S. Alonso-Quesada, “Stable multi-estimation model for single-input single-output discrete adaptive control systems,” International Journal of Systems Science, vol. 35, no. 8, pp. 479–501, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. De la Sen and S. Alonso-Quesada, “Model matching via multirate sampling with fast sampled input guaranteeing the stability of the plant zeros: extensions to adaptive control,” IET Control Theory & Applications, vol. 1, no. 1, pp. 210–225, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Liang and M. Ishitobi, “Properties of zeros of discretised system using multirate input and hold,” IEE Proceedings: Control Theory and Applications, vol. 151, no. 2, pp. 180–184, 2004. View at Publisher · View at Google Scholar
  9. 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
  10. B. Iričanin and S. Stević, “On some rational difference equations,” Ars Combinatoria, vol. 92, pp. 67–72, 2009. View at MathSciNet
  11. S. Stević, “On a generalized max-type difference equation from automatic control theory,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1841–1849, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, NJ, USA, 1989.
  13. P. A. Ioannou and Datta, “Robust adaptive control: a unified approach,” Proceedings of the IEEE, vol. 79, no. 12, pp. 1736–1768, 1991. View at Publisher · View at Google Scholar · View at Scopus
  14. R. H. Middleton, G. C. Goodwin, D. J. Hill, and D. Q. Mayne, “Design issues in adaptive control,” IEEE Transactions on Automatic Control, vol. 33, no. 1, pp. 50–58, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. Alonso-Quesada and M. De la Sen, “Robust adaptive control with multiple estimation models for stabilization of a class of non-inversely stable time-varying plants,” Asian Journal of Control, vol. 6, no. 1, pp. 59–73, 2004.
  16. K. G. Arvanitis, “An algorithm for adaptive pole placement control of linear systems based on generalized sampled-data hold functions,” Journal of the Franklin Institute, vol. 336, no. 3, pp. 503–521, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. J. Błachuta, “On approximate pulse transfer functions,” IEEE Transactions on Automatic Control, vol. 44, no. 11, pp. 2062–2067, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. L. Chen and L. Chen, “Permanence of a discrete periodic Volterra model with mutual interference,” Discrete Dynamics in Nature and Society, vol. 20089, Article ID 205481, 9 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y.-H. Fan and L.-L. Wang, “Permanence for a discrete model with feedback control and delay,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 945109, 8 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. C. Wei and L. Chen, “A delayed epidemic model with pulse vaccination,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 746951, 12 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. H. R. Karimi, M. Zapateiro, and N. Luo, “New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations,” Mathematical Problems in Engineering, vol. 2009, Article ID 759248, 22 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. G. Tao and P. A. Ioannou, “Model reference adaptive control for plants with unknown relative degree,” IEEE Transactions on Automatic Control, vol. 38, no. 6, pp. 976–982, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  23. G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, Englewood Cliffs, NJ, USA, 1984.
  24. C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, New York, NY, USA, 1975. View at MathSciNet