Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 679460, 13 pages
http://dx.doi.org/10.1155/2014/679460
Research Article

A Delay Decomposition Approach to the Stability Analysis of Singular Systems with Interval Time-Varying Delay

Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China

Received 4 May 2014; Revised 25 June 2014; Accepted 26 June 2014; Published 13 July 2014

Academic Editor: Yuxin Zhao

Copyright © 2014 Jianmin Jiao and Rui Zhang. 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. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Birkhauser, Boston, Mass, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  2. E. Fridman and U. Shaked, “An improved stabilization method for linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1931–1937, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. W. Qian, S. Cong, Y. Sun, and S. Fei, “Novel robust stability criteria for uncertain systems with time-varying delay,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 866–872, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. X. M. Zhang and Q. L. Han, “A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays,” International Journal of Robust and Nonlinear Control, vol. 19, no. 17, pp. 1922–1930, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. J. Kim, “Note on stability of linear systems with time-varying delay,” Automatica, vol. 47, no. 9, pp. 2118–2121, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. P. Liu, “State feedback stabilization of time-varying delay uncertain systems: a delay decomposition approach,” Linear Algebra and Its Applications, vol. 438, no. 5, pp. 2188–2209, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Y. He, Q. Wang, C. Lin, and M. Wu, “Delay-range-dependent stability for systems with time-varying delay,” Automatica, vol. 43, no. 2, pp. 371–376, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. W. Zhang, X. Cai, and Z. Han, “Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations,” Journal of Computational and Applied Mathematics, vol. 234, no. 1, pp. 174–180, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. H. Y. Shao, “New delay-dependent stability criteria for systems with interval delay,” Automatica, vol. 45, no. 3, pp. 744–749, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. P. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays,” Automatica, vol. 47, no. 1, pp. 235–238, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. Sun, G. P. Liu, J. Chen, and D. Rees, “Improved stability criteria for linear systems with time-varying delay,” IET Control Theory & Applications, vol. 4, no. 4, pp. 683–689, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. Sun, G. P. Liu, J. Chen, and D. Rees, “Improved delay-range-dependent stability criteria for linear systems with time-varying delays,” Automatica, vol. 46, no. 2, pp. 466–470, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Y. Liu, L. Hu, and P. Shi, “A novel approach on stabilization for linear systems with time-varying input delay,” Applied Mathematics and Computation, vol. 218, no. 10, pp. 5937–5947, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. W. Qian, S. Cong, T. Li, and S. Fei, “Improved stability conditions for systems with interval time-varying delay,” International Journal of Control, Automation and Systems, vol. 10, no. 6, pp. 1146–1152, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. W. Qian and J. Liu, “New stability analysis for systems with interval time-varying delay,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 350, no. 4, pp. 890–897, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. Y. Wang, A. Yu, and X. Zhang, “Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach,” Neural Computing and Applications, vol. 23, no. 5, pp. 1217–1227, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. T. Wang, X. Zhang, and Y. He, “Improved delay-dependent robust stability criteria for a class of uncertain mixed neutral and Lur'e dynamical systems with interval time-varying delays and sector-bounded nonlinearity,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2188–2194, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. F. Li, L. Wu, and P. Shi, “Stochastic stability of semi-Markovian jump systems with mode-dependent delays,” International Journal of Robust and Nonlinear Control, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Dai, Singular Control Systems, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  20. R. Zhong and Z. Yang, “Delay-dependent robust control of descriptor systems with time delay,” Asian Journal of Control, vol. 8, no. 1, pp. 36–44, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. S. Zhou and W. X. Zheng, “Robust H control of delayed singular systems with linear fractional parametric uncertainties,” Journal of the Franklin Institute, vol. 346, no. 2, pp. 147–158, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Z. G. Wu and W. N. Zhou, “Delay-dependent robust H control for uncertain singular time-delay systems,” IET Control Theory & Applications, vol. 1, no. 5, pp. 1234–1241, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. L. L. Liu, J. G. Peng, and B. W. Wu, “H control of singular time-delay systems via discretized Lyapunov functional,” Journal of the Franklin Institute, vol. 348, no. 4, pp. 749–762, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. L. Li and Y. M. Jia, “Observer-based resilient L2-L1 control for singular time-delay systems,” IET Control Theory and Applications, vol. 3, no. 10, pp. 1351–1362, 2009. View at Google Scholar
  25. E. Boukas, “Delay-dependent robust stabilizability of singular linear systems with delays,” Stochastic Analysis and Applications, vol. 27, no. 4, pp. 637–655, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. F. Li and X. Zhang, “A delay-dependent bounded real lemma for singular {LPV} systems with time-variant delay,” International Journal of Robust and Nonlinear Control, vol. 22, no. 5, pp. 559–574, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  27. J. Jiao, “A stability criterion for singular systems with two additive time-varying delay components,” International Journal of Automation and Computing, vol. 10, no. 1, pp. 39–45, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. J. Lin and S. Fei, “Reliable control for a class of uncertain singular systems with interval time-varying delay,” Asian Journal of Control, vol. 13, no. 4, pp. 542–552, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. J. Jiao, “Delay-dependent stability criteria for singular systems with interval time-varying delay,” Mathematical Problems in Engineering, vol. 2012, Article ID 570834, 16 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  30. F. Li and X. Zhang, “Delay-range-dependent robust H filtering for singular LPV systems with time variant delay,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 1, pp. 339–353, 2013. View at Google Scholar · View at Scopus
  31. J. Jiao, “Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty,” International Journal of Automation and Computing, vol. 9, no. 1, pp. 8–15, 2012. View at Publisher · View at Google Scholar · View at Scopus
  32. X. Zhang and H. Y. Zhu, “Robust stability and stabilization criteria for discrete singular time-delay LPV systems,” Asian Journal of Control, vol. 14, no. 4, pp. 1084–1094, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. H. Zhu, X. Zhang, and S. Cui, “Further results on H control for discrete-time uncertain singular systems with interval time-varying delays in state and input,” Optimal Control Applications & Methods, vol. 34, no. 3, pp. 328–347, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. F. B. Li, P. Shi, L. G. Wu et al., “Fuzzy-model-based D-Stability and non-fragile control for discrete-time descriptor systems with multiple delays,” IEEE Transactions on Fuzzy Systems, 2013, 10.1109/TFUZZ.2013.227264 7. View at Google Scholar