Skip to main content
SpringerLink
Log in

Sliding Mode Control of Uncertain Stochastic Hybrid Delay Systems with Average Dwell Time

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper investigates the problem of sliding mode control (SMC) for uncertain switched stochastic system with time-varying delay. The system under consideration is concerned with the stochastic dynamics and deterministic switching laws. An integral sliding surface is constructed and the stable sliding mode is derived. A sufficient condition for mean-square exponential stability of the sliding mode is developed under a class of switching laws based on the average dwell time method. Variable structure controllers are designed to guarantee the existence of the sliding mode from the initial time. An illustrative example is used to demonstrate the effectiveness of the proposed scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Benzaouia, F. Tadeo, Stabilization of positive switching linear discrete-time systems. Int. J. Innov. Comput. Inf. Control 6(6), 2427–2438 (2010)

    Google Scholar 

  2. M.L. Bujorianu, J. Lygeros, General stochastic hybrid systems: modeling and optimal control, in 43rd IEEE Conference on Decision and Control (2004), pp. 1872–1877

    Google Scholar 

  3. W. Cao, J. Xu, Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems. IEEE Trans. Autom. Control 49(8), 1355–1360 (2004)

    Article  MathSciNet  Google Scholar 

  4. D. Cheng, L. Guo, Y. Lin, Stabilization of switched linear systems. IEEE Trans. Autom. Control 50(5), 661–666 (2005)

    Article  MathSciNet  Google Scholar 

  5. J. Daafouz, P. Riedinger, C. Iung, Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Control 47(11), 1883–1887 (2002)

    Article  MathSciNet  Google Scholar 

  6. E. de Souza, X. Li, Delay-dependent robust H ∞ control for uncertain linear with state-delay systems. Automatica 35, 1313–1321 (2008)

    Article  Google Scholar 

  7. M. Defoort, T. Floquet, W. Perruquetti, S.V. Drakunov, Integral sliding mode control of an extended Heisenberg system. IET Control Theory Appl. 3(10), 1409–1424 (2009)

    Article  MathSciNet  Google Scholar 

  8. Y. Dong, J. Sun, On hybrid control of a class of stochastic non-linear Markovian switching systems. Automatica 44, 990–995 (2008)

    Article  MathSciNet  Google Scholar 

  9. D. Du, B. Jiang, P. Shi, Active fault-tolerant control for switched systems with time delay. Int. J. Adapt. Control Signal Process. 25(5), 466–480 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Giua, C. Seatzu, Optimal control of switched autonomous linear systems, in Proceedings of the 40th IEEE Conference on Decision and Control (2001), pp. 2472–2477

    Google Scholar 

  11. J. Hu, J. Lygeros, S. Sastry, Towards a theory of stochastic hybrid systems, in Hybrid Systems: Computation and Control, vol. 1790 (Springer, New York, 2000), pp. 160–173

    Chapter  Google Scholar 

  12. S. Laghrouche, F. Plestan, A. Glumineau, Higher order sliding mode control based on integral sliding mode. Automatica 43, 531–537 (2007)

    Article  MathSciNet  Google Scholar 

  13. Z. Li, C. Wen, Y.C. Soh, Stabilization of a class of switched systems via designing switching laws. IEEE Trans. Autom. Control 46(4), 665–670 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Lian, J. Zhao, Output feedback variable structure control for a class of uncertain switched systems. Asian J. Control 11(1), 31–39 (2009)

    Article  MathSciNet  Google Scholar 

  15. J. Lian, J. Zhao, G.M. Dimirovski, Integral sliding mode control for a class of uncertain switched nonlinear systems. Eur. J. Control 16(1), 16–22 (2010)

    Article  MathSciNet  Google Scholar 

  16. D. Liberzon, Switching in Systems and Control (Brikhäuser, Boston, 2003)

    Book  MATH  Google Scholar 

  17. D. Liberzon, A.S. Morse, Basic problem in stability and design of switched systems. IEEE Control Syst. 19(5), 59–70 (1999)

    Article  Google Scholar 

  18. Y. Niu, D.W.C. Ho, J. Lam, Robust integral sliding mode control for uncertain stochastic systems with time-varying delay. Automatica 41, 873–880 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. H. Pang, G. Tang, Global robust optimal sliding mode control for a class of nonlinear systems with uncertainties. ICIC Express Lett. 4(6(B)), 2501–2508 (2010)

    Google Scholar 

  20. E. Seah, I. Hwang, Stochastic linear hybrid systems: modeling, estimation and application in air traffic control. IEEE Trans. Control Syst. Technol. 17(3), 563–575 (2009)

    Article  Google Scholar 

  21. P. Shi, Y. Xia, G.P. Liu, D. Rees, On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51(1), 97–103 (2006)

    Article  MathSciNet  Google Scholar 

  22. Z. Sun, S. Ge, Switched Linear Systems-Control and Design (Springer, New York, 2005)

    MATH  Google Scholar 

  23. Z. Sun, S. Ge, T.H. Lee, Controllability and reachability criteria for switched linear systems. Automatica 38(5), 775–786 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. V. Utkin, J. Shi, Integral sliding mode in systems operating under uncertainty conditions, in Proceedings of the 35th Conference on Decision and Control (1996), pp. 4591–4596

    Google Scholar 

  25. D. Wang, W. Wang, P. Shi, Exponential H ∞ filtering for switched linear systems with interval time-varying delay. Int. J. Robust Nonlinear Control 19, 532–551 (2009)

    Article  MATH  Google Scholar 

  26. L. Wu, D.W.C. Ho, Reduced-order L 2–L ∞ filtering for a class of nonlinear switched stochastic systems. IET Control Theory Appl. 3(5), 493–508 (2009)

    Article  MathSciNet  Google Scholar 

  27. L. Wu, J. Lam, Sliding mode control of switched hybrid systems with time-varying delay. Int. J. Adapt. Control Signal Process. 22, 909–931 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. D. Wang, P. Shi, W. Wang, Robust fault detection for continue-time switched delay systems: an linear matrix approach. IET Control Theory Appl. 4(1), 100–108 (2010)

    Article  MathSciNet  Google Scholar 

  29. Y. Xia, Y. Jia, Robust sliding-mode control for uncertain time-delay systems: an LMI approach. IEEE Trans. Autom. Control 48(6), 1086–1092 (2003)

    Article  MathSciNet  Google Scholar 

  30. W. Xiang, F. Chen, Sliding mode control strategies for the hyperchaotic MCK system. ICIC Express Lett. 3(3(A)), 283–288 (2009)

    Google Scholar 

  31. Z. Xi, T. Hesketh, Discrete time integral sliding mode control for systems with matched and unmatched uncertainties. IET Control Theory Appl. 4(5), 889–896 (2010)

    Article  MathSciNet  Google Scholar 

  32. G. Xie, L. Wang, Controllability and stabilizability of switched linear-systems. Syst. Control Lett. 48(2), 135–155 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  33. L. Yu, S. Fei, H. Zu, X. Li, Direct adaptive neural control with sliding mode method for a class of uncertain switched nonlinear systems. Int. J. Innov. Comput. Inf. Control 6(12), 5609–5618 (2010)

    Google Scholar 

  34. G. Zhai, R. Kou, J. Imae, T. Kobayashi, Stability analysis and design for switched descriptor systems. Int. J. Control. Autom. Syst. 7(3), 349–355 (2009)

    Article  Google Scholar 

  35. L. Zhang, B. Jiang, Stability of a class of switched linear systems with uncertainties and average dwell time switching. Int. J. Innov. Comput. Inf. Control 6(2), 667–676 (2010)

    Google Scholar 

  36. L. Zhang, P. Shi, Stability, l 2-gain and asynchronous H ∞ control of discrete-time switched systems with average dwell time. IEEE Trans. Autom. Control 54(9), 2193–2200 (2009)

    MathSciNet  Google Scholar 

  37. L. Zhang, E. Boukas, P. Shi, Z. Chen, A μ-dependent approach to H ∞ control of uncertain switched linear systems with average dwell time. Optim. Control Appl. Methods 32(1), 15–27 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  38. J. Zhao, J.D. Hill, On stability and L 2 gain for switched systems, in Proceedings of the 44th IEEE Conference on Decision and Control (2005), pp. 3279–3284

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Jie Lian & Feng Zhang

  2. Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd, CF37 1DL, UK

    Peng Shi

  3. School of Engineering and Science, Victoria University, Melbourne, VIC, 8001, Australia

    Peng Shi

Authors
  1. Jie Lian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jie Lian.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lian, J., Zhang, F. & Shi, P. Sliding Mode Control of Uncertain Stochastic Hybrid Delay Systems with Average Dwell Time. Circuits Syst Signal Process 31, 539–553 (2012). https://doi.org/10.1007/s00034-011-9336-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-011-9336-3

Keywords

Search

Navigation