Stability and Stabilization of NCSs

Chapter

Abstract

Closed control loops in communication networks are becoming more and more common as network hardware becomes cheaper and use of the Internet expands. Feedback control systems in which control loops are closed through a real-time network are called NCSs. In an NCS, network-induced delays of variable length occur during data exchange between devices (sensor, controller, actuator) connected to the network. This can degrade the performance of the control system and can even destabilize it [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. It is important to make these delays bounded and as small as possible. On the other hand, it is also necessary to design a controller that guarantees the stability of an NCS for delays less than the maximum allowable delay bound (MADB) [12], which is also called the maximum allowable transfer interval (MATI) [5, 6].

Keywords

IEEE Transaction Network Control System Gain Matrix Stop Condition Cone Complementarity Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Y. Chow and Y. Tipsuwan. Gain adaptation of networked DC motor controllers on QoS variations. IEEE Transactions on Industrial Electronics, 50(5): 936–943, 2003.CrossRefGoogle Scholar
  2. 2.
    K. C. Lee, K. Lee, and M. H. Lee. QoS-based remote control of networked control systems via profibus token passing protocol. IEEE Transactions on Industrial Informatics, 1(3): 183–191, 2005.CrossRefGoogle Scholar
  3. 3.
    K. C. Lee, K. Lee, and M. H. Lee. Worst case communication delay of real-time industrial switched Ethernet with multiple levels. IEEE Transactions on Industrial Electronics, 53(5): 1669–1676, 2006.CrossRefGoogle Scholar
  4. 4.
    Y. Tipsuwan and M. Y. Chow. Gain scheduler middleware: a methodology to enable existing controllers for networked control and teleoperation-part I: networked control. IEEE Transactions on Industrial Electronics, 51(6): 1228–1237, 2004.CrossRefGoogle Scholar
  5. 5.
    G. Walsh, O. Beldiman, and L. Bushnell. Asymptotic behavior of nonlinear networked control systems. IEEE Transactions on Automatic Control, 46(7): 1093–1097, 2001.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    G. Walsh, H. Ye, and L. Bushnell. Stability analysis of networked control systems. IEEE Transactions on Control Systems Technology, 10(3): 438–446, 2002.CrossRefGoogle Scholar
  7. 7.
    F. W. Yang, Z. D. Wang, Y. S. Hung, and M. Gani. H∞ control for networked systems with random communication delays. IEEE Transactions on Automatic Control, 51(3): 511–518, 2006.CrossRefMathSciNetGoogle Scholar
  8. 8.
    T. C. Yang. Networked control systems: a brief survey. IEE Proceedings—Control Theory & Applications, 153(4): 403–412, 2006.CrossRefGoogle Scholar
  9. 9.
    W. Zhang, M. S. Branicky, and S. M. Phillips. Stability of networked control systems. IEEE Control Systems Magazine, 21(1): 84–99, 2001.CrossRefGoogle Scholar
  10. 10.
    H. Gao, T. Chen, and J. Lam. A new delay system approach to network-based control. Automatica, 44(1): 39–52, 2008.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    H. Gao and T. Chen. Network-Based H∞ Output Tracking Control. IEEE Transactions on Automatic Control, 53(3): 655–667, 2008CrossRefMathSciNetGoogle Scholar
  12. 12.
    D. Kim, Y. Lee, W. Kwon, and H. Park. Maximum allowable delay bounds of networked control systems. Control Engineering Practice, 11, 1301–1313, 2003.CrossRefGoogle Scholar
  13. 13.
    K. Gu, V. L. Kharitonov, and J. Chen. Stability of Time-Delay Systems. Boston: Birkhäuser, 2003.MATHGoogle Scholar
  14. 14.
    H. Gao, J. Lam, C. Wang, and Y. Wang. Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay. IEE Proceedings—Control Theory & Applications, 151(6): 691–698, 2004.CrossRefMathSciNetGoogle Scholar
  15. 15.
    C. Lin, Q. G. Wang, and T. H. Lee. A less conservative robust stability test for linear uncertain time-delay systems. IEEE Transactions on Automatic Control, 51(1): 87–91, 2006.CrossRefMathSciNetGoogle Scholar
  16. 16.
    X. Jiang and Q. L. Han. On H∞ control for linear systems with interval time-varying delay. Automatica, 41(12): 2099–2106, 2005.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    E. K. Boukas and N. F. Al-Muthairi. Delay-dependent stabilization of singular linear systems with delays. International Journal of Innovative Computing, Information and Control, 2(2): 283–291, 2006.Google Scholar
  18. 18.
    X. M. Zhang, M. Wu, J. H. She, and Y. He. Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica, 41(8): 1405–1412, 2005.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    E. Fridman and U. Shaked. Delay-dependent stability and H∞ control: constant and time-varying delays. International Journal of Control, 76(1): 48–60, 2003.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    H. Gao and C. Wang. Comments and further results on “A descriptor system approach to H∞ control of linear time-delay systems”. IEEE Transactions on Automatic Control, 48(3): 520–525, 2003.CrossRefMathSciNetGoogle Scholar
  21. 21.
    Q. L. Han. On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty. Automatica, 40(6): 1087–1092, 2004.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    M. Wu, Y. He, J. H. She, and G. P. Liu. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica, 40(8): 1435–1439, 2004.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Y. He, M. Wu, J. H. She, and G. P. Liu. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Transactions on Automatic Control, 49(5): 828–832, 2004.CrossRefMathSciNetGoogle Scholar
  24. 24.
    H. Park, Y. Kim, D. Kim, and W. Kwon. A scheduling method for network based control systems. IEEE Transactions on Control Systems Technology, 10(3): 318–330, 2002.CrossRefGoogle Scholar
  25. 25.
    Y. J. Pan, H. J. Marquez, and T. Chen. Stabilization of remote control systems with unknown time-varying delays by LMI techniques. International Journal of Control, 79(7): 752–763, 2006.MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    D. Yue, Q. L. Han, and C. Peng. State feedback controller design of networked control systems. IEEE Transactions on Circuits and Systems II, 51(11): 640–644, 2004.CrossRefGoogle Scholar
  27. 27.
    M. Wu, Y. He, and J. H. She. New delay-dependent stability criteria and stabilizing method for neutral systems. IEEE Transactions on Automatic Control, 49(12): 2266–2271, 2004.CrossRefMathSciNetGoogle Scholar
  28. 28.
    D. Yue, Q. L. Han, and J. Lam. Network-based robust H∞ control of systems with uncertainty. Automatica, 41(6): 999–1007, 2005.MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Y. He, Q. G. Wang, L. H. Xie, and C. Lin. Further improvement of freeweighting matrices technique for systems with time-varying delay. IEEE Transactions on Automatic Control, 52(2): 293–299, 2007.CrossRefMathSciNetGoogle Scholar
  30. 30.
    Y. He, Q. G. Wang, C. Lin, and M. Wu. Delay-range-dependent stability for systems with time-varying delay. Automatica, 43(2): 371–376, 2007.MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    S. Xu, J. Lam, and Y. Zou. New results on delay-dependent robust H∞ control for systems with time-varying delays. Automatica, 42(2): 343–348, 2006.MATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    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, 74(14): 1447–1455, 2001.MATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Y. He, G. P. Liu, D. Rees, and M. Wu. Improved stabilization method for networked control systems. IET Control Theory & Applications, 1(6): 1580–1585, 2007.CrossRefGoogle Scholar
  34. 34.
    Y. He, Q. G. Wang, C. Lin, and M. Wu. Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems. International Journal of Robust and Nonlinear Control, 15(18): 923–933, 2005.MATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    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, 152(2): 147–151, 2005.CrossRefMathSciNetGoogle Scholar
  36. 36.
    E. L. Ghaoui, F. Oustry, and M. AitRami. A cone complementarity linearization algorithms for static output feedback and related problems. IEEE Transactions on Automatic Control, 42(8): 1171–1176, 1997.MATHCrossRefGoogle Scholar

Copyright information

© Science Press Beijing and Springer-Verlag Berlin Heidelberg 2010

Personalised recommendations