Skip to main content
SpringerLink
Log in

Sliding Mode Multiobserver for Time-Varying Delay Nonlinear Systems Based on Discrete Uncoupled Multimodel

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

Abstract

The present paper deals with the design of sliding mode multiobserver for nonlinear systems with delayed measurements. The discrete uncoupled state multimodel is exploited to describe the global behavior of nonlinear systems. Therefore, the complexity of the latter can be reduced by its decomposition into a finite number of partial models. The proposed sliding mode multiobserver is designed based on this uncoupled multimodel approach. Sufficient conditions are formulated in terms of linear matrix inequalities in order to ensure the asymptotic stability of the designed multiobserver. Illustrative examples are included to show the effectiveness of the proposed strategy.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. A. Akhenak, M. Chadli, J. Ragot, D. Maquin, Fault detection and isolation using sliding mode observer for uncertain Takagi–Sugeno fuzzy model, in 16th Mediterranean Conference on Control and Automation (IEEE , 2008), pp. 286–291

  2. Y. Ariba, F. Gouaisbaut, Construction of Lyapunov–Krasovskii functional for time-varying delay systems, in 2008 47th IEEE Conference on Decision and Control (IEEE, 2008), pp. 3995–4000

  3. S. Ben Atia, A. Messaoud, R. Ben Abdennour, Robust multiobserver design for discrete uncertain nonlinear systems with time-varying delay. Trans. Inst. Measur. Control 40(1), 191–201 (2018)

    Google Scholar 

  4. S. Ben Atia, A. Messaoud, M. Ltaief, R. Ben Abdennour, Synthesis of multi-observers for discrete-time nonlinear systems with delayed output. Int. J. Sci. Tech. Autom. Control Comput. Eng. 8(1), 1966–1981 (2014)

    Google Scholar 

  5. P.A. Bliman, Lmi characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov–Krasovskii functionals. Syst. Control Lett. 43(4), 263–274 (2001)

    MathSciNet  MATH  Google Scholar 

  6. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics (SIAM), vol. 15 (Addison-Wesley, Philadelphia, 1994)

    MATH  Google Scholar 

  7. D. Breda, S. Maset, R. Vermiglio, Pseudospectral differencing methods for characteristic roots of delay differential equations. SIAM J. Sci. Comput. 27(2), 482–495 (2005)

    MathSciNet  MATH  Google Scholar 

  8. Y.Y. Cao, P.M. Frank, Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst. 8(2), 200–211 (2000)

    Google Scholar 

  9. Y.Y. Cao, P.M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy Sets Syst. 124(2), 213–229 (2001)

    MathSciNet  MATH  Google Scholar 

  10. C.C. De Wit, J.J. Slotine, Sliding observers for robot manipulators. Automatica 27(5), 859–864 (1991)

    MathSciNet  Google Scholar 

  11. K. Dehri, M. Ltaief, A.S. Nouri, Discrete second order sliding mode control for nonlinear multivariable systems, in 16th IEEE Mediterranean Electrotechnical Conference (MELECON) (2012), pp. 387–390

  12. R. Dey, G. Ray, S. Ghosh, A. Rakshit, Stability analysis for continuous system with additive time-varying delays: a less conservative result. Appl. Math. Comput. 215(10), 3740–3745 (2010)

    MathSciNet  MATH  Google Scholar 

  13. C. Dorling, A. Zinober, A comparative study of the sensitivity of observers, in Proceeding Symposium on Applied Control and Identification, Copenhagen (1983), pp. 32–37

  14. E. Edjekouane, S. Riachy, M. Ghanes, J.P. Barbot, Homogeneous control of pneumatic cylinders based on time delay model and artstein transformation. Asian J. Control 19(2), 792–798 (2017)

    MathSciNet  MATH  Google Scholar 

  15. C. Edwards, S. Spurgeon, Sliding Mode Control: Theory and Applications (CRC Press, Boca Raton, 1998)

    MATH  Google Scholar 

  16. C. Edwards, S.K. Spurgeon, On the development of discontinuous observers. Int. J. Control 59, 1211–1229 (1994)

    MathSciNet  MATH  Google Scholar 

  17. D. Filev, Fuzzy modeling of complex systems. Int. J. Approx. Reason. 5, 281–290 (1991)

    MATH  Google Scholar 

  18. E. Fridman, New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems. Syst. Control Lett. 43(4), 309–319 (2001)

    MathSciNet  MATH  Google Scholar 

  19. A. Germani, C. Manes, P. Pepe, A new approach to state observation of nonlinear systems with delayed output. IEEE Trans. Autom. Control 47(1), 96–101 (2002)

    MathSciNet  MATH  Google Scholar 

  20. K. Gu, J. Chen, V.L. Kharitonov, Stability of time-Delay Systems (Springer, Berlin, 2003)

    MATH  Google Scholar 

  21. K. Hfaïedh, K. Dahech, T. Damak, A sliding mode observer for uncertain nonlinear systems based on multiple models approach. Int. J. Autom. Comput. 14(2), 202–212 (2017)

    Google Scholar 

  22. A. Hurwitz, Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt, in Mathematische Werke (Springer, Basel, 1963), pp. 533–545

  23. P. Kachroo, M. Tomizuka, Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems. IEEE Trans. Autom. Control 41(7), 1063–1068 (1996)

    MathSciNet  MATH  Google Scholar 

  24. R. Kalman, A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82, 35–45 (1960)

    MathSciNet  Google Scholar 

  25. H.R. Karimi, M. Chadli, Robust observer design for Takagi-Sugeno fuzzy systems with mixed neutral and discrete delays and unknown inputs. Math. Prob. Eng. 2012, 1–13 (2012)

    MathSciNet  MATH  Google Scholar 

  26. N. Kazantzis, R.A. Wright, Nonlinear observer design in the presence of delayed output measurements. Syst. Control Lett. 54(9), 877–886 (2005)

    MathSciNet  MATH  Google Scholar 

  27. D. Kharrat, H. Gassara, A. El Hajjaji, M. Chaabane, Adaptive fuzzy observer-based fault-tolerant control for Takagi–Sugeno descriptor nonlinear systems with time delay. Circ. Syst. Signal Process. 37(4), 1542–1561 (2018)

    MathSciNet  MATH  Google Scholar 

  28. V.B. Kolmanovskii, J.P. Richard, Stability of some linear systems with delays. IEEE Trans. Autom. Control 44(5), 984–989 (1999)

    MathSciNet  MATH  Google Scholar 

  29. A.J. Koshkouei, A.S.I. Zinober, Sliding mode state observers for discrete-time linear systems. Int. J. Syst. Sci. 33(9), 751–758 (2002)

    MathSciNet  MATH  Google Scholar 

  30. A.J. Koshkouei, A.S.I. Zinober, Sliding mode controller-observer design for SISO linear systems. Int. J. Syst. Sci. 29(12), 1363–1373 (2007)

    MATH  Google Scholar 

  31. H. Li, Y. Gao, P. Shi, X. Zhao, Output-feedback control for t-s fuzzy delta operator systems with time-varying delays via an input-output approach. IEEE Trans. Fuzzy Syst. 23(4), 1100–1112 (2014)

    Google Scholar 

  32. H. Li, J. Wang, L. Wu, H.K. Lam, Y. Gao, Optimal guaranteed cost sliding-mode control of interval type-2 fuzzy time-delay systems. IEEE Trans. Fuzzy Syst. 26(1), 246–257 (2017)

    Google Scholar 

  33. C. Lin, Q.G. Wang, T.H. Lee, A less conservative robust stability test for linear uncertain time-delay systems. IEEE Trans. Autom. Control 51(1), 87–91 (2006)

    MathSciNet  MATH  Google Scholar 

  34. D.G. Luenberger, An introduction to observers. IEEE Trans. Autom. Control 16(6), 596–602 (1971)

    Google Scholar 

  35. D. Marquardt, An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11(2), 431–441 (1963)

    MathSciNet  MATH  Google Scholar 

  36. A. Messaoud, R.B. Abdennour, An experimental validation of a new method for multimodel identification. J. Dyn. Syst. Measur. Control 140(2), 024502 (2018)

  37. M. Mihoub, A. Messaoud, M. Ltaïef, A.S. Nouri, R. Ben Abdennour, Fuzzy discontinuous term for a second order asymptotic DSMC: an experimental validation on a chemical reactor. Asian J. Control 13(3), 369–381 (2011)

    MathSciNet  MATH  Google Scholar 

  38. S. Mondié, V.L. Kharitonov, Exponential estimates for retarded time-delay systems: an LMI approach. IEEE Trans. Autom. Control 50(2), 268–273 (2005)

    MathSciNet  MATH  Google Scholar 

  39. N. Montacer, K. Dehri, S. Ben Atia, R. Ben Abdennour, A sliding mode multiobserver based on an uncoupled multimodel: an application on a transesterification reaction. Asian J. Control 21(1), 1–17 (2019)

    MathSciNet  MATH  Google Scholar 

  40. R. Orjuela, B. Marx, D. Maquin, J. Ragot, Nonlinear system identification using heterogeneous multiple models. Int. J. Appl. Math. Comput. Sci. 23(1), 103–115 (2013)

    MathSciNet  MATH  Google Scholar 

  41. R. Orjuela, B. Marx, J. Ragot, D. Maquin, A decoupled multiple model approach for state estimation of nonlinear systems subject to delayed measurements. IFAC Proc. Vol. 40(21), 97–102 (2007)

    Google Scholar 

  42. R. Palm, P. Bergsten, Sliding mode observer for a takagi sugeno fuzzy system, in The 9th IEEE International Conference on Fuzzy Systems, 2000. FUZZ IEEE 2000, vol. 2, (IEEE, 2000), pp. 665–670

  43. A. Poznyak, Advanced Mathematical Tools for Automatic Control Engineers: volume 1: Deterministic Systems (Elsevier, Amsterdam, 2008)

    Google Scholar 

  44. R. Rajamani, Observer for lipschitz nonlinear systems. IEEE Trans. Autom. Control 43(3), 397–401 (1984)

    MathSciNet  MATH  Google Scholar 

  45. J.P. Richard, Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)

    MathSciNet  MATH  Google Scholar 

  46. O. Sename, New trends in design of observers for time-delay systems. Kybernetika 37(4), 427–458 (2001)

    MathSciNet  MATH  Google Scholar 

  47. S.H. Tsai, A global exponential fuzzy observer design for time-delay takagi-sugeno uncertain discrete fuzzy bilinear systems with disturbance. IEEE Trans. Fuzzy Syst. 20(6), 1063–1075 (2012)

    Google Scholar 

  48. J. Wang, H. Zhu, C.L. Zhang, Z. Chen, Y. Huang, W. Chen, X. Huang, F. Wang, Adaptive hyperbolic tangent sliding-mode control for building structural vibration systems for uncertain earthquakes. IEEE Access 6, 74728–74736 (2018)

    Google Scholar 

  49. R.J. Wang, Observer-based fuzzy control of fuzzy time-delay systems with parametric uncertainties. Int. J. Syst. Sci. 35(12), 671–683 (2004)

    MathSciNet  MATH  Google Scholar 

  50. H. Yang, M. Saif, Observer design and fault diagnosis for state-retarded dynamical systems. Automatica 34(2), 217–227 (1998)

    MathSciNet  MATH  Google Scholar 

  51. Q. Zong, F. Zeng, W. Liu, Y. Ji, Y. Tao, Sliding mode observer-based fault detection of distributed networked control systems with time delay. Circ. Syst. Signal Process. 31(1), 203–222 (2012)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by Ministry of Higher Education and Scientific Research—Tunisia.

Author information

Authors and Affiliations

  1. Research Laboratory: Numerical Control of Industrial Processes, National School of Engineers of Gabes (ENIG), University of Gabes, Omar Ibn Khattab Street, 6029, Gabés, Tunisia

    Nesrine Montacer, Samah Ben Atia, Khadija Dehri & Ridha Ben Abdennour

Authors
  1. Nesrine Montacer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Samah Ben Atia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Khadija Dehri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ridha Ben Abdennour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nesrine Montacer.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Montacer, N., Ben Atia, S., Dehri, K. et al. Sliding Mode Multiobserver for Time-Varying Delay Nonlinear Systems Based on Discrete Uncoupled Multimodel. Circuits Syst Signal Process 40, 626–647 (2021). https://doi.org/10.1007/s00034-020-01506-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-020-01506-7

Keywords

Search

Navigation