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Mathematical Problems in Engineering
Volume 2013, Article ID 517258, 8 pages
http://dx.doi.org/10.1155/2013/517258
Research Article

Stability Bound Analysis and Synthesis for Singularly Perturbed Systems with Time-Varying Delay

1Institute of Systems Science, Northeastern University, Shenyang 110819, China
2School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China
3Mathematics Department, Jilin Normal University, Siping 136000, China

Received 22 September 2012; Revised 25 December 2012; Accepted 29 December 2012

Academic Editor: Baocang Ding

Copyright © 2013 Fengqi Sun 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. C. Yang and Q. Zhang, “Multiobjective control for T-S fuzzy singularly perturbed systems,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 1, pp. 104–115, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. H. Liu, F. Sun, K. He, and Z. Sun, “Survey of singularly perturbed control systems: theory and applications,” Journal of Control Theory and Applications, vol. 20, no. 1, pp. 1–7, 2003. View at Google Scholar
  3. S. He, F. Da, and W. You, “Research advances of time-delay control theory,” Journal of Nanjing University of Science and Technology, vol. 29, pp. 132–136, 2005. View at Google Scholar
  4. S. Cong and Z. Sheng, “On exponential stability conditions of descriptor systems with time-varying delay,” Journal of Applied Mathematics, vol. 2012, Article ID 532912, 12 pages, 2012. View at Publisher · View at Google Scholar
  5. M. da la Sen, “Quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays,” Applied Mathematics and Computation, vol. 185, no. 1, pp. 508–526, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  6. V. Y. Glizer, “Euclidean space controllability of singularly perturbed linear systems with state delay,” Systems & Control Letters, vol. 43, no. 3, pp. 181–191, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. V. Y. Glizer, “Observability of singularly perturbed linear time-dependent differential systems with small delay,” Journal of Dynamical and Control Systems, vol. 10, no. 3, pp. 329–363, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. V. Y. Glizer, “Novel controllability conditions for a class of singularly-perturbed systems with small state delays,” Journal of Optimization Theory and Applications, vol. 137, no. 1, pp. 135–156, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. V. Y. Glizer and E. Fridman, “Stability of singularly perturbed functional-differential systems: spectrum analysis and LMI approaches,” IMA Journal of Mathematical Control and Information, vol. 29, no. 1, pp. 79–111, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. V. Y. Glizer and E. Fridman, “H control of linear singularly perturbed systems with small state delay,” Journal of Mathematical Analysis and Applications, vol. 250, no. 1, pp. 49–85, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. W. Luse, “Multivariable singularly perturbed feedback systems with time delay,” IEEE Transactions on Automatic Control, vol. 32, no. 11, pp. 990–994, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Z. Shao and J. R. Rowland, “Stability of time-delay singularly perturbed systems,” IEE Proceedings, vol. 142, no. 2, pp. 111–113, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. S. T. Pan, F. H. Hsiao, and C. C. Teng, “Stability bound of multiple time delay singularly perturbed systems,” Electronics Letters, vol. 32, no. 14, pp. 1327–1328, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Shao, “Robust stability of singularly perturbed systems with state delays,” IEE Proceedings, vol. 150, no. 1, pp. 2–6, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. S. B. Stojanovic and J. Debel, “Delay-dependent stability analysis for discrete-time systems with time varying state delay,” Chemical Industry and Chemical Engineering Quarterly, vol. 17, pp. 497–504, 2011. View at Google Scholar
  16. L. L. Liu, J. P. Peng, and B. W. Wu, “Robust stability of singularly perturbed systems with state delays,” in Proceedings of the International Workshop on Information Security and Application (IWISA '09), pp. 19–21, Qingdao, China, November 2009. View at Publisher · View at Google Scholar
  17. 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 Zentralblatt MATH · View at MathSciNet
  18. L. L. Liu, J. G. Peng, and B. W. Wu, “Delay-dependent criteria for robust stability of singularly perturbed systems with delays,” in Proceedings of the International Conference on Computational and Information Sciences (ICCIS '10), pp. 1–4, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. J.-S. Chiou, “Stability bound of discrete multiple time-delay singularly perturbed systems,” International Journal of Systems Science, vol. 37, no. 14, pp. 1069–1076, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. P.-L. Liu, “Stabilization of singularly perturbed multiple-time-delay systems with a saturating actuator,” International Journal of Systems Science, vol. 32, no. 8, pp. 1041–1045, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. W.-H. Chen, S.-T. Yang, X. Lu, and Y. Shen, “Exponential stability and exponential stabilization of singularly perturbed stochastic systems with time-varying delay,” International Journal of Robust and Nonlinear Control, vol. 20, no. 18, pp. 2021–2044, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. P. Mei, C. X. Cai, and Y. Zou, “Stability analysis for singularly perturbed systems with time-varying delay,” Journal of Nanjing University of Science and Technology, vol. 33, no. 3, pp. 297–301, 2009. View at Google Scholar · View at Scopus
  23. Z. H. Shao, “Stability bounds of singularly perturbed delay systems,” IEE Proceedings, vol. 151, pp. 585–588, 2004. View at Google Scholar
  24. J.-H. Kim, “Robust stability of linear systems with delayed perturbations,” IEEE Transactions on Automatic Control, vol. 41, no. 12, pp. 1820–1822, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. P. Suthee and K. Furuta, “Memoryless stabilization of uncertain linear systems including time-varying state delays,” IEEE Transactions on Automatic Control, vol. 34, pp. 460–462, 1989. View at Google Scholar
  26. Y.-Y. Cao and Y.-X. Sun, “Robust stabilization of uncertain systems with time-varying multistate delay,” IEEE Transactions on Automatic Control, vol. 43, no. 10, pp. 1484–1488, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. M. De la Sen, “On positivity of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate point delays,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 382–401, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S. L. Campbell, “A general form for solvable linear time varying singular systems of differential equations,” SIAM Journal on Mathematical Analysis, vol. 18, no. 4, pp. 1101–1115, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet