http://iet.metastore.ingenta.com
1887

Controller synthesis for one-sided Lipschitz Markovian jump systems with partially unknown transition probabilities

Controller synthesis for one-sided Lipschitz Markovian jump systems with partially unknown transition probabilities

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

A controller design method is presented for one-sided Lipschitz Markovian jump systems with partially unknown transition probabilities. By using the proposed controllers, it can be guaranteed that the state trajectories starting from a given region remain in it (without disturbances) or a bigger one (under disturbances), where the local one-sided Lipschitz and quadratically inner-bounded conditions can be satisfied. In addition, an observer-based controller is designed to stabilise the system without the requirement that the system states are measurable. Finally, two examples are given to illustrate the effectiveness of the proposed scheme.

References

    1. 1)
      • 1. Zhang, X., Polycarpou, M.M., Parisini, T.: ‘Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation’, Automatica, 2010, 46, (2), pp. 290299.
    2. 2)
      • 2. Pertew, A.M., Marquez, H.J., Zhao, Q.: ‘H observer design for Lipschitz nonlinear systems’, IEEE Trans. Autom. Control, 2006, 51, (7), pp. 12111216.
    3. 3)
      • 3. Rajamani, R.: ‘Observers for Lipschitz nonlinear systems’, IEEE Trans. Autom. Control, 1998, 43, (3), pp. 397401.
    4. 4)
      • 4. Raghavan, S., Hedrick, J.K.: ‘Observer design for a class of nonlinear systems’, Int. J. Control, 1994, 59, (2), pp. 515528.
    5. 5)
      • 5. Zhang, X.: ‘Sensor bias fault detection and isolation in a class of nonlinear uncertain systems using adaptive estimation’, IEEE Trans. Autom. Control, 2011, 56, (5), pp. 12201226.
    6. 6)
      • 6. Li, Y., Tong, S., Li, T.: ‘Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation’, IEEE Trans. Cybern., 2015, 45, (10), pp. 22992308.
    7. 7)
      • 7. Huo, B., Li, Y., Tong, S.: ‘Fuzzy adaptive fault-tolerant output feedback control of multi-input and multi-output non-linear systems in strict-feedback form’, IET Control Theory Appl., 2012, 6, (17), pp. 27042715.
    8. 8)
      • 8. Gao, Z., Ding, S.X.: ‘Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems’, Automatica, 2007, 43, (5), pp. 912920.
    9. 9)
      • 9. Zhang, W., Su, H., Zhu, F., et al: ‘A note on observers for discrete-time Lipschitz nonlinear systems’, IEEE Trans. Circ. Syst. II: Express Briefs, 2012, 59, (2), pp. 123127.
    10. 10)
      • 10. Hu, G.-D.: ‘Observers for one-sided Lipschitz non-linear systems’, IMA J. Math. Control Inf., 2006, 23, (4), pp. 395401.
    11. 11)
      • 11. Zhao, Y., Tao, J., Shi, N.-Z.: ‘A note on observer design for one-sided Lipschitz nonlinear systems’, Syst. Control Lett., 2010, 59, (1), pp. 6671.
    12. 12)
      • 12. Abbaszadeh, M., Marquez, H.J.: ‘Nonlinear observer design for one-sided Lipschitz systems’. Proc. 2010 American Control Conf. IEEE, 2010, pp. 52845289.
    13. 13)
      • 13. Song, J., He, S.: ‘Robust finite-time H control for one-sided Lipschitz nonlinear systems via state feedback and output feedback’, J. Franklin Inst., 2015, 352, (8), pp. 32503266.
    14. 14)
      • 14. Beikzadeh, H., Marquez, H.J.: ‘Observer-based H control using the incremental gain for one-sided Lipschitz nonlinear systems’. 2014 IEEE American Control Conf. (ACC), 2014, pp. 46534658.
    15. 15)
      • 15. Zhang, W., Su, H., Zhu, F., et al: ‘Unknown input observer design for one-sided Lipschitz nonlinear systems’, Nonlinear Dyn., 2015, 79, (2), pp. 14691479.
    16. 16)
      • 16. Benallouch, M., Boutayeb, M., Zasadzinski, M.: ‘Observer design for one-sided Lipschitz discrete-time systems’, Syst. Control Lett., 2012, 61, (9), pp. 879886.
    17. 17)
      • 17. Nguyen, M.C., Trinh, H.: ‘Reduced-order observer design for one-sided Lipschitz time-delay systems subject to unknown inputs’, IET Control Theory Appl., 2016, 10, (10), pp. 10971105.
    18. 18)
      • 18. Beikzadeh, H., Marquez, H.J.: ‘Sampled-data observer for one-sided lipschitz systems: Single-rate and multirate cases’. 2015 IEEE American Control Conference (ACC), 2015, pp. 33863391.
    19. 19)
      • 19. Shi, P., Li, F.: ‘A survey on Markovian jump systems: modeling and design’, Int. J. Control, Autom. Syst., 2015, 13, (1), pp. 116.
    20. 20)
      • 20. Wu, L., Su, X., Shi, P.: ‘Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems’, Automatica, 2012, 48, (8), pp. 19291933.
    21. 21)
      • 21. Shen, M.: ‘H filtering of continuous Markov jump linear system with partly known Markov modes and transition probabilities’, J. Franklin Inst., 2013, 350, (10), pp. 33843399.
    22. 22)
      • 22. Fan, Q.-Y., Yang, G.-H., Ye, D.: ‘Adaptive tracking control for a class of Markovian jump systems with time-varying delay and actuator faults’, J. Franklin Inst., 2015, 352, (5), pp. 19792001.
    23. 23)
      • 23. Li, L.-W., Yang, G.-H.: ‘Fault estimation for a class of nonlinear Markov jump systems with general uncertain transition rates’, Int. J. Syst. Sci., 2016, pp. 113.
    24. 24)
      • 24. Shen, H., Su, L., Park, J.H.: ‘Extended passive filtering for discrete-time singular Markov jump systems with time-varying delays’, Analog Integr. Circ. Signal Process., 2016, 128, pp. 6877.
    25. 25)
      • 25. Zhang, L., Boukas, E.-K.: ‘Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities’, Automatica, 2009, 45, (2), pp. 463468.
    26. 26)
      • 26. Shen, H., Su, L., Park, J.H.: ‘Further results on stochastic admissibility for singular Markov jump systems using a dissipative constrained condition’, ISA Trans., 2015, 59, pp. 6571.
    27. 27)
      • 27. Shen, M., Yan, S., Zhang, G., et al: ‘Finite-time H static output control of Markov jump systems with an auxiliary approach’, Appl. Math. Comput., 2016, 273, pp. 553561.
    28. 28)
      • 28. Zhang, L., Boukas, E.-K., Lam, J.: ‘Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities’, IEEE Trans. Autom. Control, 2008, 53, (10), pp. 24582464.
    29. 29)
      • 29. Kwon, N.K., Park, B.Y., Park, P.: ‘Less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation’, Opt. Control Appl. Methods, 2016, 37, (6), pp. 12071216. Available at http://dx.doi.org/10.1002/oca.2233.
    30. 30)
      • 30. Beikzadeh, H., Marquez, H.J.: ‘Input-to-error stable observer for nonlinear sampled-data systems with application to one-sided Lipschitz systems’, Automatica, 2016, 67, pp. 17.
    31. 31)
      • 31. Liu, H., Boukas, E.-K., Sun, F., et al: ‘Controller design for Markov jumping systems subject to actuator saturation’, Automatica, 2006, 42, (3), pp. 459465.
    32. 32)
      • 32. Mao, X.: ‘Stability of stochastic differential equations with Markovian switching’, Stoch. Processes Appl., 1999, 79, (1), pp. 4567.
    33. 33)
      • 33. Yang, H., Shi, P., Li, Z., et al: ‘Analysis and design for delta operator systems with actuator saturation’, Int. J. Control, 2014, 87, (5), pp. 987999.
    34. 34)
      • 34. Li, X., Zhu, F., Chakrabarty, A., et al: ‘Non-fragile fault-tolerant fuzzy observer-based controller design for nonlinear systems’, IEEE Trans. Fuzzy Syst., 2016, PP, (99), pp. 11.
    35. 35)
      • 35. Hu, T., Lin, Z.: ‘Control systems with actuator saturation: analysis and design’ (Springer Science & Business Media, 2001).
    36. 36)
      • 36. Zhang, Y., He, Y., Wu, M., et al: ‘Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices’, Automatica, 2011, 47, (1), pp. 7984.
    37. 37)
      • 37. Li, Y., Sun, H., Zong, G., Hou, L.: ‘Disturbance-observer-based-control and L2L resilient control for Markovian jump non-linear systems with multiple disturbances and its application to single robot arm system’, IET Control Theory Appl., 2016, 10, (2), pp. 226233.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.1425
Loading

Related content

content/journals/10.1049/iet-cta.2016.1425
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address