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Mathematical Problems in Engineering
Volume 2015, Article ID 456768, 7 pages
http://dx.doi.org/10.1155/2015/456768
Research Article

Finite Frequency Filtering for Time-Delayed Singularly Perturbed Systems

1Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China
2Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing, Jiangsu 210044, China

Received 18 September 2014; Revised 29 January 2015; Accepted 16 February 2015

Academic Editor: Thomas Hanne

Copyright © 2015 Ping Mei 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. A. Tahar and M. N. Abdelkrim, “Multimodel H loop shaping control of a DC motor under variable loads,” in Proceedings of the 8th International Multi-Conference on Systems, Signals & Devices (SSD '11), pp. 1–6, IEEE, Sousse, Tunisia, March 2011. View at Publisher · View at Google Scholar · View at Scopus
  2. N. Abdelkrim, A. Tellili, and M. N. Abdelkrim, “Additive fault tolerant control applied to delayed singularly perturbed system,” Journal of Software Engineering and Applications, vol. 5, no. 4, pp. 217–224, 2012. View at Publisher · View at Google Scholar
  3. P. Mei, J. Fu, Y. Gong, and Z. Zhang, “Generalized H2 control for fast sampling discrete-time fuzzy singularly perturbed systems,” ICIC Express Letters, vol. 5, no. 4, pp. 1487–1493, 2011. View at Google Scholar · View at Scopus
  4. W.-H. Chen, G. Yuan, and W. X. Zheng, “Robust stability of singularly perturbed impulsive systems under nonlinear perturbation,” IEEE Transactions on Automatic Control, vol. 58, no. 1, pp. 168–174, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. T. Nguyen, W.-C. Su, and Z. Gajic, “Variable structure control for singularly perturbed linear continuous systems with matched disturbances,” IEEE Transactions on Automatic Control, vol. 57, no. 3, pp. 777–783, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. H. Gao and X. Li, “H filtering for discrete-time state-delayed systems with finite frequency specifications,” IEEE Transactions on Automatic Control, vol. 56, no. 12, pp. 2935–2941, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. P. Shi, E.-K. Boukas, and R. K. Agarwal, “Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters,” IEEE Transactions on Automatic Control, vol. 44, no. 8, pp. 1592–1597, 1999. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Wang and G.-H. Yang, “A finite frequency approach to filter design for uncertain discrete-time systems,” International Journal of Adaptive Control and Signal Processing, vol. 22, no. 6, pp. 533–550, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. X. Shen, M. Rao, and Y. Ying, “Decomposition method for solving the gains of Kalman filter in singularly perturbed systems,” in Proceedings of the American Control Conference, pp. 3350–3354, 1992.
  10. M. D. S. Aliyu and E. K. Boukas, “H2 filtering for non-linear singularly perturbed systems,” IET Control Theory and Applications, vol. 5, no. 17, pp. 2023–2032, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. X. Shen and L. Deng, “Decomposition solution of H filter gain in singularly perturbed systems,” Signal Processing, vol. 55, no. 3, pp. 313–320, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. E. Fridman, “Effects of small delays on stability of singularly perturbed systems,” Automatica, vol. 38, no. 5, pp. 897–902, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. V. Y. Glizer, “Controllability of nonstandard singularly perturbed systems with small state delay,” IEEE Transactions on Automatic Control, vol. 48, no. 7, pp. 1280–1285, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. V. Y. Glizer, “On stabilization of nonstandard singularly perturbed systems with small delays in state and control,” IEEE Transactions on Automatic Control, vol. 49, no. 6, pp. 1012–1016, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y.-J. Kim, B.-S. Kim, and M.-T. Lim, “Composite control for singularly perturbed bilinear systems via successive Galerkin approximation,” IEE Proceedings: Control Theory and Applications, vol. 150, no. 5, pp. 483–488, 2003. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Iwasaki and S. Hara, “Generalized KYP lemma: unified frequency domain inequalities with design applications,” IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 41–59, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. T. Iwasaki and S. Hara, “Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma,” International Journal of Robust and Nonlinear Control, vol. 17, no. 5-6, pp. 415–434, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. H. G. Hoang, H. D. Tuan, and T. Q. Nguyen, “Frequency-selective KYP lemma, IIR filter, and filter bank design,” IEEE Transactions on Signal Processing, vol. 57, no. 3, pp. 956–965, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. P. Mei and Y. Zou, “Finite frequency positive realness analysis of singularly perturbed systems based on generalized KYP lemma approach,” Control and Decision, vol. 25, no. 5, pp. 711–714, 2010 (Chinese). View at Google Scholar · View at MathSciNet
  20. P. Mei, C. Cai, and Y. Zou, “A generalized KYP lemma-based approach for H control of singularly perturbed systems,” Circuits, Systems, and Signal Processing, vol. 28, no. 6, pp. 945–957, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Y. Huang, C. Cai, and Y. Zou, “Finite frequency positive real control for singularly perturbed systems,” International Journal of Control, Automation and Systems, vol. 9, no. 2, pp. 376–383, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. H. Wang and G.-H. Yang, “Fault detection observer design for linear discrete-time systems in finite frequency domain,” in Proceedings of the 46th IEEE Conference on Decision and Control (CDC '07), pp. 378–383, New Orleans, Lo, USA, December 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. C. Du, L. Xie, G. Guo, and J. Nee Teoh, “A generalized KYP lemma based approach for disturbance rejection in data storage systems,” Automatica, vol. 43, no. 12, pp. 2112–2118, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. P. Balasubramaniam, V. M. Revathi, and J. H. Park, “L2-L filtering for neutral Markovian switching system with mode-dependent time-varying delays and partially unknown transition probabilities,” Applied Mathematics and Computation, vol. 219, no. 17, pp. 9524–9542, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. V. M. Revathi, P. Balasubramaniam, J. H. Park, and T. H. Lee, “H filtering for sample data systems with stochastic sampling and Markovian jumping parameters,” Nonlinear Dynamics, vol. 78, no. 2, pp. 813–830, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  26. P. Gahinet and P. Apkarian, “A linear matrix inequality approach to H control,” International Journal of Robust and Nonlinear Control, vol. 4, no. 4, pp. 421–448, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus