Decentralised Variable Structure Control for Time Delay Interconnected Systems

  • Xing-Gang YanEmail author
  • Sarah K. Spurgeon
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 440)


A class of multiple time varying delay interconnected systems with nonlinear disturbances is considered in this Chapter, where both the known and uncertain interconnections involve time delay. A decentralised static output feedback variable structure control is synthesised, which is independent of the time delays, to stabilise the system globally uniformly asymptotically. The stability of the closed loop system is analysed based on the Lyapunov Razumikhin approach. Then, for interconnected systems where each subsystem is square, it is shown that the effects of the uncertain interconnections can be largely rejected by appropriate controllers if the delays are known and the uncertain interconnections are bounded by a class of functions of the outputs and delayed outputs. A case study relating to a river pollution control problem is presented to illustrate the proposed approach.


Biochemical Oxygen Demand Slide Mode Control Output Feedback Interconnected System Output Feedback Control 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bakule, L.: Decentralized control: an overview. Annual Reviews in Control 32(1), 87–98 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Edwards, C., Akoachere, A., Spurgeon, S.K.: Sliding-mode output feedback controller design using linear matrix inequalities. IEEE Trans. on Automat. Control 46(2), 115–119 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Edwards, C., Spurgeon, S.K.: Sliding mode control: theory and applications. Taylor and Francis Ltd., London (1998)Google Scholar
  4. 4.
    Edwards, C., Yan, X.G., Spurgeon, S.K.: On the solvability of the constrained Lyapunov problem. IEEE Trans. on Automat. Control 52(10), 1982–1987 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Galimidi, A.R., Barmish, B.R.: The constrained Lyapunov problem and its application to robust output feedback stabilization. IEEE Trans. on Automat. Control 31(5), 410–419 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Gu, K., Kharitonov, V.L., Chen, J.: Stability of time-delay systems. Birkhäuser, Boston (2003)zbMATHCrossRefGoogle Scholar
  7. 7.
    Hsu, K.C.: Decentralized variable-structure control design for uncertain large-scale systems with series nonlinearities. Int. J. Control 68(6), 1231–1240 (1997)zbMATHCrossRefGoogle Scholar
  8. 8.
    Hua, C., Ding, S.X.: Model following controller design for large-scale systems with time-delay interconnections and multiple dead-zone inputs. IEEE Trans. on Automat. Control 56(4), 962–968 (2011)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hua, C., Guan, X.: Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks. IEEE Trans. on Neural Networks 19(4), 673–688 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hua, C.C., Wang, Q.G., Guan, X.P.: Memoryless state feedback controller design for time delay systems with matched uncertain nonlinearities. IEEE Trans. on Automat. Control 53(3), 801–807 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jain, S., Khorrami, F.: Decentralized adaptive output feedback design for large-scale nonlinear systems. IEEE Trans. on Automat. Control 42(5), 729–735 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Jiang, Z.P.: Decentralized disturbance attenuating output-feedback trackers for large-scale nonlinear systems. Automatica 38(8), 1407–1415 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Lee, J.L.: On the decentralized stabilization of interconnected variable structure systems using output feedback. Journal of the Franklin Institute 332(5), 595–605 (1995)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Lunze, J.: Feedback control of Large scale systems. Prentice Hall International (UK) Ltd., Hemel Hempstead (1992)zbMATHGoogle Scholar
  15. 15.
    Mirkin, B.M., Gutman, P.: Decentralized output-feedback MRAC of linear state delay systems. IEEE Trans. on Automat. Control 48(9), 1613–1619 (2003)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Mahmoud, M.S.: Decentralized output-feedback stabilization for interconnected discrete systems with unknown delays. Optimal Control Applications & Methods 31(6), 529–545 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Mahmoud, M.S.: Decentralized Systems with Design Constraints. Springer-Verlag London Limited (2011)Google Scholar
  18. 18.
    Mahmoud, M.S., Bingulac, S.: Robust design of stabilizing controllers for interconnected time-delay systems. Automatica 34(5), 795–800 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Michiels, W., Niculescu, S.I.: Stability and stabilization of time-delay systems: an eigenvalue-based approach. The Society for Industrial and Applied Mathematics, Philadelphia (2007)zbMATHCrossRefGoogle Scholar
  20. 20.
    Panagi, P., Polycarpou, M.M.: Decentralized fault tolerant control of a class of interconnected nonlinear systems. IEEE Trans. on Automat. Control 56(1), 178–184 (2011)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Richard, J.P.: Time-delay systems: An overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Rodellar, J., Leitmann, G., Ryan, E.P.: Output feedback control of uncertain coupled systems. Int. J. Control 58(2), 445–457 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Saberi, A., Khalil, H.: Decentralized stabilization of interconnected systems using output feedback. Int. J. Control 41(6), 1461–1475 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Sandell, N.R., Varaiya, P., Athans, M., Safonov, M.G.: Survey of decentralized control methods for large-scale systems. IEEE Trans. on Automat. Control 23(2), 108–128 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Utkin, V.I.: Sliding modes in control optimization. Springer, Berlin (1992)zbMATHCrossRefGoogle Scholar
  26. 26.
    Xie, S., Xie, L.: Decentralized stabilization of a class of interconnected stochastic nonlinear systems. IEEE Trans. on Automat. Control 45(1), 132–137 (2000)zbMATHCrossRefGoogle Scholar
  27. 27.
    Yan, X.G., Edwards, C., Spurgeon, S.K.: Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback. Automatica 40(4), 613–620 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Yan, X.G., Spurgeon, S.K., Edwards, C.: Decentralised sliding mode control for nonminimum phase interconnected systems based on a reduced-order compensator. Automatica 42(10), 1821–1828 (2006)zbMATHCrossRefGoogle Scholar
  29. 29.
    Yan, X.G., Spurgeon, S.K., Edwards, C.: Sliding mode control for time-varying delayed systems based on a reduced-order observer. Automatica 46(8), 1354–1362 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Yan, X.G., Spurgeon, S.K., Edwards, C.: Global decentralised static output feedback sliding mode control for interconnected time-delay systems. IET Control Theory and Applications 6(2), 192–202 (2012)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Yan, X.G., Wang, J., Lü, X., Zhang, S.: Decentralized output feedback robust stabilization for a class of nonlinear interconnected systems with similarity. IEEE Trans. on Automat. Control 43(2), 294–299 (1998)zbMATHCrossRefGoogle Scholar
  32. 32.
    Zak, S.H., Hui, S.: Output feedback variable structure controllers and state estimators for uncertain/nonlinear dynamic systems. IEE Proc. Part D: Control Theory Appl. 140(1), 41–50 (1993)CrossRefGoogle Scholar
  33. 33.
    Zhou, J.: Decentralized adaptive control for large-scale time-delay systems with dead-zone input. Automatica 44(7), 1790–1799 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Zhou, J., Wen, C.: Decentralized backstepping adaptive output tracking of interconnected nonlinear systems. IEEE Trans. on Automat. Control 53(10), 2378–2384 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Instrumentation, Control and Embedded Systems Research Group, School of Engineering and Digital ArtsUniversity of KentCanterburyUnited Kingdom

Personalised recommendations