Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 790521, 9 pages
http://dx.doi.org/10.1155/2014/790521
Research Article

Robust Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China

Received 22 July 2014; Revised 18 September 2014; Accepted 23 September 2014; Published 27 November 2014

Academic Editor: Mathiyalagan Kalidass

Copyright © 2014 Li-li Liu 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. L. Dai, Singular Control Systems, Springer, Berlin, Germany, 1989.
  2. S. Xu and J. Lam, Robust Control and Filtering of Singular Systems, Springer, Berlin, Germany, 2006. View at MathSciNet
  3. S. Xu, J. Lam, and C. Yang, “Robust H\sb control for uncertain singular systems with state delay,” International Journal of Robust and Nonlinear Control, vol. 13, no. 13, pp. 1213–1223, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. J. H. Kim, “New design method on memoryless H\sb control for singular systems with delayed state and control using LMI,” Journal of the Franklin Institute, vol. 342, no. 3, pp. 321–327, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. 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
  6. E. Fridman and U. Shaked, “H control of linear state-delay descriptor systems: an LMI approach,” Linear Algebra and Its Applications, vol. 351-352, pp. 271–302, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  7. E. Fridman and U. Shaked, “A descriptor system approach to H control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 253–270, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. D. Yue and Q.-L. Han, “Delay-dependent robust H controller design for uncertain descriptor systems with time-varying discrete and distributed delays,” IEE Proceedings: Control Theory and Applications, vol. 152, no. 6, pp. 628–638, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. E. K. Boukas, “Singular linear systems with delays: H stabilization,” Optimal Control Applications & Methods, vol. 28, no. 4, pp. 259–274, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. Z. Wu and W. 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
  11. S. Xu, J. Lam, and Y. Zou, “An improved characterization of bounded realness for singular delay systems and its applications,” International Journal of Robust and Nonlinear Control, vol. 18, no. 3, pp. 263–277, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. M. Fang, “Delay-dependent robust H control for uncertain singular systems with state delay,” Acta Automatica Sinica, vol. 35, no. 1, pp. 65–70, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. R. Sakthivel, S. Santra, and K. Mathiyalagan, “Admissibility analysis and control synthesis for descriptor systems with random abrupt changes,” Applied Mathematics and Computation, vol. 219, no. 18, pp. 9717–9730, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. R. Sakthivel, S. Srimanta, K. Mathiyalagan, and A. Arunkumar, “Reliable robust control design for uncertain mechanical systems,” Journal of Dynamical Systems, Measurement and Control, vol. 137, no. 2, Article ID 021003, 11 pages, 2014. View at Publisher · View at Google Scholar
  15. Z.-G. Wu, H.-Y. Su, and J. Chu, “Improved results on delay-dependent H control for singular time-delay systems,” Acta Automatica Sinica, vol. 35, no. 8, pp. 1101–1106, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. L. Liu, J. Peng, and B. 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
  17. K. Gu, “Discretized LMI set in the stability problem of linear uncertain time-delay systems,” International Journal of Control, vol. 68, no. 4, pp. 923–934, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. P. Shi, Y. Yin, and F. Liu, “Gain-scheduled worst-case control on nonlinear stochastic systems subject to actuator saturation and unknown information,” Journal of Optimization Theory and Applications, vol. 156, no. 3, pp. 844–858, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. S. Wen, Z. Zeng, T. Huang, and Y. Zhang, “Exponential lag adaptive synchronization of memristive neural networks and applications in Pseudo-random generators,” IEEE Transactions on Fuzzy Systems, 2013. View at Publisher · View at Google Scholar
  20. S. Wen, Z. Zeng, and T. Huang, “H filtering for neutral systems with mixed delays and multiplicative noises,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 59, no. 11, pp. 820–824, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. S. P. Wen, Z. G. Zeng, T. W. Huang, and C. J. Li, “Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays,” International Journal of Robust and Nonlinear Control, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Wen, Z. Zeng, T. Huang, and G. Bao, “Robust passivity and passification for a class of singularly perturbed nonlinear systems with time-varying delays and polytopic uncertainties via neural networks,” Circuits, Systems, and Signal Processing, vol. 32, no. 3, pp. 1113–1127, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Systems & Control Letters, vol. 8, no. 4, pp. 351–357, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus