access icon free Robust observer-based finite-time control for one-sided Lipschitz singular systems with uncertainties

© The Institution of Engineering and Technology
Received 08/08/2019, Accepted 29/06/2020, Revised 28/05/2020, Published 06/08/2020

This study deals with the problem of observer-based finite-time control for a class of one-sided Lipschitz (OSL) singular systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and output matrices but also in the non-linear function. With the help of some special derivations and transformation, the sufficient conditions ensuring robust finite-time boundedness of the closed-loop system and satisfying the performance index are given for OSL singular systems in terms of linear matrix inequalities (LMIs). Based on these, the observer and controller dynamics can be simultaneously involved in the design at one step. Two convex optimisation problems subject to LMIs are formulated to optimise the desired performance indices of interest to us. Finally, two examples are given to demonstrate the effectiveness of the proposed methods.

Inspec keywords: nonlinear functions; robust control; linear matrix inequalities; observers; uncertain systems; closed loop systems; convex programming

Other keywords: robust observer-based finite-time H∞ control; time-varying norm-bounded uncertainties; closed-loop system; one-sided Lipschitz singular systems; linear matrix inequalities; parameter uncertainties; robust finite-time boundedness; nonlinear function; controller dynamics; output matrices; OSL singular systems; convex optimisation problems

Subjects: Optimal control; Algebra; Stability in control theory; Optimisation techniques

References

    1. 1)
      • 46. Thanh, N.T., Niamsup, P., Phat, V.N.: ‘Finite-time stability of singular nonlinear switched time-delay systems: a singular value decomposition approach’, J. Franklin Inst., 2017, 354, (8), pp. 3502–3518.
    2. 2)
      • 16. Zhang, W., Su, H.S., Liang, Y., et al: ‘Non-linear observer design for one-sided Lipschitz systems: an linear matrix inequality approach’, IET Control Theory Applic., 2012, 6, (9), pp. 1297–1303.
    3. 3)
      • 49. Uezato, E., Ikeda, M.: ‘Strict LMI conditions for stability, robust stabilization, and H∞ control of descriptor systems’. Proc. 38th Conf. on Decision and Control, Phoenix, Arizona, USA, 1999, vol. 4, pp. 4092–4097.
    4. 4)
      • 11. Ruderman, M., Iwasaki, M.: ‘Control of nonlinear elastic joint robots using feed-forward torque decoupling’, IFAC PapersOnline, 2015, 48, (11), pp. 137–142.
    5. 5)
      • 35. Zhang, Y., Liu, C., Mu, X.: ‘Robust finite-time stabilization of uncertain singular Markovian jump systems’, Appl. Math. Model., 2012, 36, (10), pp. 5109–5121.
    6. 6)
      • 48. Liu, C., Zhang, Y., Sun, H.: ‘Finite-time H∞ filtering for singular stochastic systems’, J. Appl. Math., 2012, 2012, (3), pp. 30–33.
    7. 7)
      • 12. Qi, W., Zong, G., Karim, H.R.: ‘Observer-based adaptive SMC for nonlinear uncertain singular semi-Markov jump systems with applications to dc motor’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2018, 65, (9), pp. 2951–2960.
    8. 8)
      • 3. Wang, G., Zhang, Q., Yan, X.: ‘Analysis and design of singular Markovian jump systems’ (Springer, Berlin, Germany, 2015).
    9. 9)
      • 7. Zhang, Y., Shi, P., Nguang, S.K., et al: ‘Robust finite-time H∞ control for uncertain discrete-time singular systems with Markovian jumps’, IET Control Theory Applic., 2014, 8, (12), pp. 1105–1111.
    10. 10)
      • 30. Tian, J., Ma, S., Zhang, C.: ‘Unknown input reduced-order observer design for one-sided Lipschitz nonlinear descriptor Markovian jump systems’, Asian J. Control, 2019, 21, (2), pp. 952–964.
    11. 11)
      • 28. Zulfiqar, A., Rehan, M., Abid, M.: ‘Observer design for one-sided Lipschitz descriptor systems’, Appl. Math. Model., 2016, 40, (3), pp. 2301–2311.
    12. 12)
      • 8. Zhang, Y., Shi, P., Nguang, S.K.: ‘Observer-based finite-time H∞ control for discrete singular stochastic systems’, Appl. Math. Lett., 2014, 38, pp. 115–121.
    13. 13)
      • 21. Nguyen, C.M., Pathirana, P.N., Trinh, H.: ‘Robust observer design for uncertain one-sided Lipschitz systems with disturbances’, Int. J. Robust Nonlinear Control, 2018, 28, (4), pp. 1366–1380.
    14. 14)
      • 39. 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. 3250–3266.
    15. 15)
      • 18. Barbata, A., Zasadzinski, M., Souley-Ali, H., et al: ‘Exponential observer for a class of one-sided Lipschitz stochastic nonlinear systems’, IEEE Trans. Autom. Control, 2015, 60, (1), pp. 259–264.
    16. 16)
      • 19. Zhang, W., Su, H., Zhu, F., et al: ‘Improved exponential observer design for one-sided Lipschitz nonlinear systems’, Int. J. Robust Nonlinear Control, 2016, 26, (18), pp. 3958–3973.
    17. 17)
      • 33. Ma, Y., Jia, X., Zhang, Q.: ‘Robust finite-time non-fragile memory H∞ control for discrete-time singular Markovian jumping systems subject to actuator saturation’, J. Franklin Inst., 2017, 354, (18), pp. 8256–8282.
    18. 18)
      • 32. Amato, F., Ariola, M., Dorato, P.: ‘Finite-time control of linear systems subject to parametric uncertainties and disturbances’, Automatica, 2001, 37, (9), pp. 1459–1463.
    19. 19)
      • 43. Ren, J., Zhang, Q.: ‘Robust normalization and guaranteed cost control for a class of uncertain descriptor systems’, Automatica,, 2012, 48, (8), pp. 1693–1697.
    20. 20)
      • 40. Huang, Y., Fu, S., Shen, Y.: ‘Finite-time H∞ control for one-sided Lipschitz systems with auxiliary matrices’, Neurocomputing, 2016, 194, pp. 207–217.
    21. 21)
      • 26. Ahmad, S., Rehan, M., Hong, K.S.: ‘Observer-based robust control of one-sided Lipschitz nonlinear systems’, ISA Trans., 2016, 65, pp. 230–240.
    22. 22)
      • 47. Abbaszadeh, M., Marquez, H.J.: ‘A generalized framework for robust nonlinear H∞ filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties’, Automatica, 2012, 48, (5), pp. 894–900.
    23. 23)
      • 50. Delshad, S.S., Johansson, A., Darouach, M., et al: ‘Robust state estimation and unknown inputs reconstruction for a class of nonlinear systems: multiobjective approach’, Automatica, 2016, 64, pp. 1–7.
    24. 24)
      • 41. Saad, W., Sellami, A., Garcia, G.: ‘Robust integral sliding mode-H∞ control of one-sided Lipschitz non-linear systems’, IET Control Theory Applic., 2018, 12, (17), pp. 2357–2367.
    25. 25)
      • 6. Zhang, Y., Shi, P., Agarwal, R.K.: ‘Event-based dissipative analysis for discrete time-delay singular stochastic systems’, Int. J. Robust Nonlinear Control, 2018, 28, (18), pp. 6106–6121.
    26. 26)
      • 20. Nam, P.T., Pathirana, P.N., Trinh, H.: ‘Discrete Wirtinger-based inequality and its application’, J. Franklin Inst., 2015, 352, (5), pp. 1893–1905.
    27. 27)
      • 23. Cai, X., Wang, Z., Liu, L.: ‘Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay’, Neurocomputing, 2015, 165, pp. 182–189.
    28. 28)
      • 2. Lei, F., Ma, Y.: ‘Passive control for singular time-delay system with actuator saturation’, Appl. Math. Comput., 2016, 289, pp. 181–193.
    29. 29)
      • 9. Osorio-Gordillo, G.L., Darouach, M., Boutat-Baddas, L., et al: ‘H∞ dynamical observer-based control for descriptor systems’, IMA J. Math. Control Inf., 2018, 35, (3), pp. 707–734.
    30. 30)
      • 25. Wu, Y., Dong, J.: ‘Controller synthesis for one-sided Lipschitz Markovian jump systems with partially unknown transition probabilities’, IET Control Theory Applic., 2017, 11, (14), pp. 2242–2251.
    31. 31)
      • 1. Jin, Z., Zhang, Q., Meng, X.: ‘The stability analysis and control of uncertain singular biological economic system with invasion of alien species based on sliding mode control’, J. Intell. Fuzzy Syst., Appl. Eng. Technol., 2018, 34, (6), pp. 4079–4091.
    32. 32)
      • 4. Xu, S., Yang, C.: ‘An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems’, Int. J. Syst. Sci., 2000, 31, (1), pp. 55–61.
    33. 33)
      • 15. Abbaszadeh, M., Marquez, H.J.: ‘Nonlinear observer design for one-sided Lipschitz systems’. Proc. American Control Conf., Anchorage, AK, USA, 2010, pp. 5284–5289.
    34. 34)
      • 24. Ahmad, S., Rehan, M.: ‘On observer-based control of one-sided Lipschitz systems’, J. Franklin Inst., 2016, 353, (4), pp. 903–916.
    35. 35)
      • 38. Song, J., He, S.: ‘Finite-time H∞ control for quasi-one-sided Lipschitz nonlinear systems’, Neurocomputing, 2015, 149, pp. 1433–1439.
    36. 36)
      • 44. Chang, X.H., Zhang, L., Park, J.H.: ‘Robust static output feedback H∞ control for uncertain fuzzy systems’, Fuzzy Sets Syst., 2015, 273, pp. 87–104.
    37. 37)
      • 42. Howell, A., Hedrick, J.K.: ‘Nonlinear observer design via convex optimization’. Proc. American Control Conf., Anchorage, AK, USA, 2002, pp. 2088–2093.
    38. 38)
      • 31. Sun, Y., Ma, S.: ‘Observer-based finite-time stabilization for discrete-time switched singular systems with quadratically inner-bounded nonlinearities’, Int. J. Robust Nonlinear Control, 2019, 29, (6), pp. 2041–2062.
    39. 39)
      • 22. Nguyen, C.M., Pathirana, P.N., Trinh, H.: ‘Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances’, Appl. Math. Comput., 2019, 353, pp. 42–53.
    40. 40)
      • 27. Haiek-Badreddine, E., Aiss-Hicham, E., Abdelaziz, H., et al: ‘New approach to robust observer-based control of one-sided Lipschitz non-linear systems’, IET Control Theory Applic., 2019, 13, (3), pp. 333–342.
    41. 41)
      • 45. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, Cambridge, UK, 1985).
    42. 42)
      • 29. Yang, Y., Lin, C., Chen, B.: ‘Nonlinear H∞ observer design for one-sided Lipschitz discrete-time singular systems with time-varying delay’, Int. J. Robust Nonlinear Control, 2019, 29, (1), pp. 252–267.
    43. 43)
      • 5. Xu, S., Lam, J.: ‘Robust control and filtering of singular systems’ (Springer, Berlin, Germany, 2006).
    44. 44)
      • 14. 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. 66–71.
    45. 45)
      • 17. Zhang, W., Su, H., Wang, H., et al: ‘Full-order and reduced-order observers for one-sided Lipschitz nonlinear systems using Riccati equations’, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, (12), pp. 4968–4977.
    46. 46)
      • 10. Han, Y., Kao, Y., Park, J.H.: ‘Robust H∞ nonfragile observer-based control of switched discrete singular systems with time-varying delays: a sliding mode control design’, Int. J. Robust Nonlinear Control, 2019, 29, (5), pp. 1462–1483.
    47. 47)
      • 37. Zhang, Y., Shi, P., Nguang, S.K., et al: ‘Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays’, Signal Process., 2014, 97, pp. 252–261.
    48. 48)
      • 34. Zong, G., Wang, R., Zheng, W., et al: ‘Finite-time H∞ control for discrete-time switched nonlinear systems with time delay’, Int. J. Robust Nonlinear Control, 2015, 25, (6), pp. 914–936.
    49. 49)
      • 13. Hu, G.D.: ‘Observers for one-sided Lipschitz non-linear systems’, IMA J. Math. Control Inf., 2006, 23, (4), pp. 395–401.
    50. 50)
      • 36. Zhang, Y., Shi, Y., Shi, P.: ‘Robust and non-fragile finite-time H∞ control for uncertain Markovian jump nonlinear systems’, Appl. Math. Comput., 2016, 279, pp. 125–138.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2019.0927
Loading

Related content

content/journals/10.1049/iet-cta.2019.0927
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading