Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Robust control for a class of non-linear discrete time-delay systems with controller failure: a probability-dependent method

  • Author(s): Hong Nie 1 ; Hong Sang 2 ; Ping Li 2
    • View affiliations
  • Source: Volume 11, Issue 17, 24 November 2017, p. 3211 – 3220
    DOI:  10.1049/iet-cta.2017.0703 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 27/06/2017, Accepted 04/09/2017, Revised 17/08/2017, Published 05/09/2017

This study addresses the issue of robust control for a class of discrete-time delayed non-linear systems in the presence of controller failure by using a probability-dependent method. Considering the stochasticity and inevitability of controller failure, they propose a notion of controller probabilistic failure. Based on the idea of switching, the studied systems are converted into a kind of stochastic switched systems. When the probability information is available, a probability-dependent switching strategy is developed by application of piecewise Lyapunov function and average dwell time approaches such that the system is exponentially mean square stable with weighted performance. At the same time, a probability-dependent weighted switching controller is designed. Moreover, the obtained results are also shown to be feasible when the probability information cannot be known accurately. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.

Inspec keywords: probability; discrete time systems; switching systems (control); stochastic systems; H∞ control; control system synthesis; nonlinear control systems; Lyapunov methods; delays; robust control; asymptotic stability

Other keywords: controller probabilistic failure; piecewise Lyapunov function; weighted switching controller; robust H∞ control; stochastic switched systems; exponentially mean square stability; probability-dependent method; nonlinear discrete time-delay systems; average dwell time approaches

Subjects: Control system analysis and synthesis methods; Optimal control; Discrete control systems; Nonlinear control systems; Time-varying control systems; Distributed parameter control systems; Other topics in statistics; Stability in control theory

References

    1. 1)
      • 28. Tian, E.G., Wong, W.K., Yue, D., et al.: ‘Filtering for discrete-time switched systems with known sojourn probabilities’, IEEE Trans. Autom. Control, 2015, 60, (9), pp. 1–6.
    2. 2)
      • 9. Cheng, C.K., Kuo, H.H., Hou, Y.Y., et al.: ‘Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays’, Physica A, 2008, 387, (13), pp. 3093–3102.
    3. 3)
      • 15. Huang, S.P., Xiang, Z.R.: ‘Robust L∞ reliable control for uncertain switched nonlinear systems with time delay under asynchronous switching’, Appl. Math. Comput., 2013, 222, (3), pp. 658–670.
    4. 4)
      • 1. Xiang, Z.R., Chen, Q.W.: ‘Robust reliable control for uncertain switched nonlinear systems with time delay under asynchronous switching’, Appl. Math. Comput., 2013, 222, (3), pp. 658–670.
    5. 5)
      • 6. Liu, X., Zhong, S.M., Ding, X.Y.: ‘Robust exponential stability of nonlinear impulsive switched systems with time-varying delays’, Nonlinear Anal. Model. Control, 2012, 17, (2), pp. 210–222.
    6. 6)
      • 2. Gao, H.J., Wang, C.H.: ‘A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems’, IEEE Trans. Signal Process., 2004, 52, (6), pp. 1631–1640.
    7. 7)
      • 25. Zhang, Y.: ‘Stability of discrete-time Markovian jump delay systems with delayed impulses and partly unknown transition probabilities’, Nonlinear Dyn., 2014, 75, (1), pp. 101–111.
    8. 8)
      • 21. Sun, X.M., Liu, G.P., Wang, W., et al: ‘L2-Gain of systems with input delays and controller temporary failure: zero-order hold model’, IEEE Trans. Control Syst. Technol., 2011, 19, (3), pp. 699–706.
    9. 9)
      • 12. Shen, B., Wang, Z.D., Shu, H.S., et al: ‘H∞ filter for nonlinear discrete-time stochastic system with randomly varying sensor delays’, Automatica, 2009, 45, (4), pp. 1032–1037.
    10. 10)
      • 23. Huang, J., Li, C., Han, Q.: ‘Stabilization of delayed chaotic neural networks by periodically intermittent control’, Circ. Syst. Signal Process., 2009, 28, (4), pp. 567–579.
    11. 11)
      • 3. González, A.: ‘Robust stabilization of linear discrete-time systems with time-varying input delay’, Automatica, 2013, 49, (9), pp. 2919–2922.
    12. 12)
      • 31. Yu, Q., Zhao, X.D.: ‘Stability analysis of discrete-time switched linear systems with unstable subsystems’, Appl. Math. Comput., 2016, 273, pp. 718–725.
    13. 13)
      • 11. Huang, S.J., He, X.Q., Zhang, N.N.: ‘New results on H∞ filter design for nonlinear systems with time delay via T-S fuzzy models’, IEEE Trans. Fuzzy Syst., 2011, 19, (1), pp. 193–199.
    14. 14)
      • 20. Xiang, W.M., Zhai, G.S., Briat, C.: ‘Stability analysis for LTI control systems with controller failures and its application in failure tolerant control’, IEEE Trans. Autom. Control, 2015, 61, (3), pp. 811–816.
    15. 15)
      • 17. Zhai, G.S., Lin, H.: ‘Controller failure time analysis for symmetric H∞ control systems’, Int. J. Control, 2004, 77, (6), pp. 598–605.
    16. 16)
      • 8. Ball, J.A., Helton, J.W., Walker, M.L.: ‘H∞ control for nonlinear systems with output feedback’, IEEE Trans. Autom. Control, 2002, 38, (4), pp. 546–559.
    17. 17)
      • 13. Zhang, W., Branicky, M.S., Phillips, S.M.: ‘Stability of networked control systems’, IEEE Control Syst. Mag., 2001, 20, (1), pp. 84–99.
    18. 18)
      • 29. Zhang, L.X., Shi, Y., Chen, T.W., et al.: ‘A new method for stabilization of networked control systems with random delays’, IEEE Trans. Autom. Control, 2005, 50, (8), pp. 1177–1181.
    19. 19)
      • 10. Lee, S.M., Ji, D.H., Park, J.H., et al.: ‘H∞ synchronization of chaotic systems via dynamic feedback approach’, Phys. Lett. A, 2008, 372, (29), pp. 4905–4912.
    20. 20)
      • 22. Zheng, S.: ‘Synchronization analysis of time delay complex-variable chaotic systems with discontinuous coupling’, J. Franklin Inst., 2016, 353, (6), pp. 1460–1477.
    21. 21)
      • 16. Hu, H., Jiang, B., Yang, H.: ‘Robust fault-tolerant control for uncertain delta operator switched systems’, IET Control Theory Appl., 2014, 8, (2), pp. 120–130.
    22. 22)
      • 26. Yang, R.N., Shi, P., Liu, G.P.: ‘Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts’, IEEE Trans. Autom. Control, 2011, 56, (11), pp. 2655–2660.
    23. 23)
      • 7. Niu, B., Zhao, J.: ‘Robust H∞ control for a class of uncertain nonlinear switched systems with average dwell time’, Int. J. Control, 2013, 86, (6), pp. 1107–1117.
    24. 24)
      • 14. Yue, D., Han, Q.L., Lam, J.: ‘Network-based robust H∞ control of systems with uncertainty’, Automatica, 2005, 41, (6), pp. 999–1007.
    25. 25)
      • 5. Lu, Q.G., Zhang, L.X., Karimi, H.R., et al: ‘H∞ control for asynchronously switched linear parameter-varying systems with mode-dependent average dwell time’, IET Control Theory Appl., 2013, 7, (5), pp. 673–683.
    26. 26)
      • 30. Zhai, G.S., Hu, B., Yasuda, K., et al.: ‘Qualitative analysis of discrete-time switched systems’. Proc 2002 American Control Conf., 2002, pp. 1880–1885.
    27. 27)
      • 18. Zhai, G.S., Chen, X.K., Takai, S., et al.: ‘Stability and H∞ disturbance attenuation analysis for LTI control systems with controller failures’, Asian J. Control, 2004, 6, (1), pp. 104–111.
    28. 28)
      • 27. Xiang, Z., Liang, C., Mahmoud, M.S.: ‘Robust H∞ filtering for discrete-time switched time-delay systems with missing measurements and asynchronous switching’, Trans. Inst. Meas. Control, 2013, 35, (2), pp. 200–211.
    29. 29)
      • 4. Feng, Z.G., Lam, J.: ‘Integral partitioning approach to robust stabilization for uncertain distributed time-delay systems’, Int. J. Robust Nonlinear Control, 2012, 22, (6), pp. 676–689.
    30. 30)
      • 24. Wang, Z.D., Ho, D.W.C., Liu, Y.R., et al.: ‘Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements’, Automatica, 2009, 45, (3), pp. 684–691.
    31. 31)
      • 19. Sun, X.M., Zhao, J., Wang, W.: ‘State feedback control for discrete delay systems with controller failures based on average dwell-time method’, IET Control Theory Appl., 2008, 2, (2), pp. 126–132.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2017.0703
Loading

Related content

content/journals/10.1049/iet-cta.2017.0703
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address