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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 585301, 8 pages
http://dx.doi.org/10.1155/2015/585301
Research Article

Robust Observer-Based Feedback Control for Lipschitz Singularly Perturbed Systems

1School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
2Center for Applied and Multidisciplinary Mathematics, Department of Mathematics, East China Normal University, Shanghai 200241, China

Received 29 April 2015; Accepted 26 July 2015

Academic Editor: Martino Bardi

Copyright © 2015 Yanyan Wang and Wei 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. P. V. Kokotović, H. K. Khalil, and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, London, UK, 1986. View at Publisher · View at Google Scholar
  2. P. Shi, S.-P. Shue, and R. K. Agarwal, “Robust disturbance attenuation with stability for a class of uncertain singularly perturbed systems,” International Journal of Control, vol. 70, no. 6, pp. 873–891, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. Z. H. Shao, “Robust stability of two-time-scale systems with nonlinear uncertainties,” IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 258–261, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. Z. H. Shao and M. E. Sawan, “Stabilisation of uncertain singularly perturbed systems,” IEE Proceedings: Control Theory and Applications, vol. 153, no. 1, pp. 99–103, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. H. Chen and J. S. Chen, “Robust composite control for singularly perturbed systems with time-varying uncertainties,” Journal of Dynamic Systems, Measurement, and Control, vol. 117, no. 4, pp. 445–452, 1995. View at Publisher · View at Google Scholar
  6. S. J. Chen and J. L. Lin, “Maximal stability bounds of singularly perturbed systems,” Journal of the Franklin Institute, vol. 336, no. 8, pp. 1209–1218, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. Z. M. Wang, W. Liu, H. H. Dai, and D. S. Naidu, “Robust stabilization of Model-based uncertain singularly perturbed systems with networked time-delay,” in Proceedings of the 48th IEEE Conference on Decision and Control, Held Jointly with the 28th Chinese Control Conference (CDC-CCC '09), pp. 7917–7922, IEEE, Shanghai, China, December 2009. View at Publisher · View at Google Scholar
  8. G. Garcia, J. Daafouz, and J. Bernussou, “H2 guaranteed cost control for singularly perturbed uncertain systems,” IEEE Transactions on Automatic Control, vol. 43, no. 9, pp. 1323–1329, 1998. View at Publisher · View at Google Scholar · View at Scopus
  9. M. G. Dmitriev and G. A. Kurina, “Singular perturbations in control problems,” Automation and Remote Control, vol. 67, no. 1, pp. 1–43, 2006. View at Google Scholar
  10. H. P. Liu, F. C. Sun, and Z. Q. Sun, “Stability analysis and synthesis of fuzzy singularly perturbed systems,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 2, pp. 273–284, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. K.-J. Lin and T.-H. S. Li, “Stabilization of uncertain singularly perturbed systems with pole-placement constraints,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 53, no. 9, pp. 916–920, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Singh, R. H. Brown, D. S. Naidu, and J. A. Heinen, “Robust stability of singularly perturbed state feedback systems using unified approach,” IEE Proceedings: Control Theory and Applications, vol. 148, no. 5, pp. 391–396, 2001. View at Publisher · View at Google Scholar · View at Scopus
  13. P. E. Moraal and J. W. Grizzle, “Observer design for nonlinear systems with discrete-time measurements,” IEEE Transactions on Automatic Control, vol. 40, no. 3, pp. 395–404, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. A. N. Atassi and H. K. Khalil, “A separation principle for the stabilization of a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 9, pp. 1672–1687, 1999. View at Publisher · View at Google Scholar · View at Scopus
  15. T. Liu, Z.-P. Jiang, and D. J. Hill, “Small-gain based output-feedback controller design for a class of nonlinear systems with actuator dynamic quantization,” IEEE Transactions on Automatic Control, vol. 57, no. 5, pp. 1326–1332, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. L. Praly and Z.-P. Jiang, “Stabilization by output feedback for systems with ISS inverse dynamics,” Systems & Control Letters, vol. 21, no. 1, pp. 19–33, 1993. View at Publisher · View at Google Scholar · View at Scopus
  17. Z. P. Jiang, D. J. Hill, and Y. Guo, “Semiglobal output feedback stabilization for the nonlinear benchmark example,” in Proceedings of the European Control Conference, Brussels, Belgium, 1997.
  18. K. R. Shouse and D. G. Taylor, “Discrete-time observers for singularly perturbed continuous-time systems,” IEEE Transactions on Automatic Control, vol. 40, no. 2, pp. 224–235, 1995. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Oloomi and M. E. Sawan, “The observer-based controller design of discrete-time singularly perturbed systems,” IEEE Transactions on Automatic Control, vol. 32, no. 3, pp. 246–248, 1987. View at Google Scholar · View at Scopus
  20. K.-J. Lin, “Composite observer-based feedback design for singularly perturbed systems via LMI approach,” in Proceedings of the SICE Annual Conference (SICE '10), pp. 3056–3061, August 2010. View at Scopus
  21. Z. M. Wang and W. Liu, “Output feedback networked control of singular perturbation,” in Proceedings of the 8th World Congress on Intelligent Control and Automation, pp. 645–650, Taipei, Taiwan, 2011.
  22. M.-Y. Shieh and J.-S. Chiou, “Design of observer and observer-based controller for a class of singularly perturbed discrete bilinear systems,” Information Technology Journal, vol. 11, no. 1, pp. 141–147, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. J.-H. Kim, “Improved quantitative measures of robustness for multivariable systems,” IEEE Transactions on Automatic Control, vol. 40, no. 9, pp. 1619–1620, 1995. View at Publisher · View at Google Scholar · View at Scopus
  24. D. M. Stipanović and D. D. Šiljak, “Robust stability and stabilization of discrete-time non-linear systems: the LMI approach,” International Journal of Control, vol. 74, no. 9, pp. 873–879, 2001. View at Publisher · View at Google Scholar · View at Scopus
  25. S. Boyd, L. E. L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994.
  26. H. K. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, USA, 2nd edition, 1996.