Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 810271, 6 pages
http://dx.doi.org/10.1155/2013/810271
Research Article

A Simplified Descriptor System Approach to Delay-Dependent Stability and Robust Performance Analysis for Discrete-Time Systems with Time Delays

Physical Education Department, Qufu Normal University, Qufu, Shandong 273165, China

Received 25 November 2012; Accepted 24 February 2013

Academic Editor: Yang Yi

Copyright © 2013 Fengying Xu and Daxin Li. 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. J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 2nd edition, 1977. View at Zentralblatt MATH · View at MathSciNet
  2. Q.-L. Han, “Robust stability of uncertain delay-differential systems of neutral type,” Automatica, vol. 38, no. 4, pp. 719–723, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. S. Mahmoud and N. F. Al-Muthairi, “Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties,” IEEE Transactions on Automatic Control, vol. 39, no. 10, pp. 2135–2139, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. H. Lee, S. W. Kim, and W. H. Kwon, “Memoryless H controllers for state delayed systems,” IEEE Transactions on Automatic Control, vol. 39, no. 1, pp. 159–162, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Xu, J. Lam, and C. Yang, “H and positive-real control for linear neutral delay systems,” IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1321–1326, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. W. Chen, Z. Guan, and X. Lu, “Delay-dependent guaranteed cost control for uncertain discretetime systems with delay,” IEE Proceedings Control Theory & Applications, vol. 150, no. 4, pp. 412–416, 2003. View at Google Scholar
  7. W.-H. Chen, Z.-H. Guan, and X. Lu, “Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays,” Journal of the Franklin Institute, vol. 341, no. 5, pp. 419–430, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. G. Zong, L. Hou, and J. Li, “A descriptor system approach to l2l filtering for uncertain discrete-time switched system with mode-dependent time-varying delays,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 5, pp. 2213–2224, 2011. View at Google Scholar
  9. G. Zong, L. Hou, and Y. Wu, “Exponential l2l filtering for discrete-time switched systems under a new framework,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 2, pp. 124–137, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. T. Li, L. Guo, and X. Xin, “Improved delay-dependent bounded real lemma for uncertain time-delay systems,” Information Sciences, vol. 179, no. 20, pp. 3711–3719, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Li, L. Guo, and L. Wu, “Simplified approach to the asymptotical stability of linear systems with interval time-varying delay,” IET Control Theory & Applications, vol. 3, no. 2, pp. 252–260, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  12. E. Fridman, “New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems,” Systems & Control Letters, vol. 43, no. 4, pp. 309–319, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. 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
  14. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, “Delay-dependent robust stabilization of uncertain state-delayed systems,” International Journal of Control, vol. 74, no. 14, pp. 1447–1455, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. Xu, J. Lam, and Y. Zou, “Simplified descriptor system approach to delay-dependent stability and performance analysis for time-delay systems,” IEE Proceedings Control Theory & Applications, vol. 152, no. 2, pp. 17–151, 2005. View at Google Scholar
  16. S. Xu and T. Chen, “Robust H control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers,” Systems & Control Letters, vol. 51, no. 3-4, pp. 171–183, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Y. S. Lee and W. H. Kwon, “Delay-Dependent robust stabilization of uncertain discrete-time state-delayed systems,” in Proceedings of the 15th IFAC Congress on Automation and Control, Barcelona, Spain, 2002.
  18. S.-H. Song, J.-K. Kim, C.-H. Yim, and H.-C. Kim, “H control of discrete-time linear systems with time-varying delays in state,” Automatica, vol. 35, no. 9, pp. 1587–1591, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet