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access icon free fuzzy filter for non-linear sampled-data systems under imperfect premise matching

© The Institution of Engineering and Technology
Received 08/03/2016, Accepted 25/12/2016, Revised 06/11/2016, Published 04/01/2017

This study proposes an fuzzy filtering technique for non-linear sampled-data systems that are represented on the basis of the Takagi–Sugeno fuzzy model. To improve the performance of the fuzzy filter, an imperfect premise matching condition is considered. An error system between the non-linear system and the fuzzy filter is constructed. In addition, sufficient conditions for showing asymptotic stability and guaranteeing disturbance attenuation performance are proposed in a Lyapunov sense and derived in terms of linear matrix inequalities. Finally, the feasibility of the proposed technique is demonstrated using two simulation examples.

Inspec keywords: pattern matching; fuzzy set theory; linear matrix inequalities; H∞ filters

Other keywords: error system; Lyapunov sense; imperfect premise matching; nonlinear sampled data systems; Takagi-Sugeno fuzzy model; H∞ fuzzy filter; linear matrix inequalities; asymptotic stability

Subjects: Combinatorial mathematics; Combinatorial mathematics; Signal processing theory; Algebra; Filtering methods in signal processing; Algebra

References

    1. 1)
      • 30. Kim, D.W., Lee, H.J.: ‘Comments on ‘T–S fuzzy-model-based robust H-infinity design for networked control systems with uncertainties’’, IEEE Trans. Ind. Inf., 2009, 5, (4), p. 507.
    2. 2)
      • 4. Li, W., Jia, Y.: ‘H-infinity filtering for a class of nonlinear discrete-time systems based on unscented transform’, Signal Process., 2010, 90, (12), pp. 3301–3307.
    3. 3)
      • 20. Kim, D.W., Lee, H.J.: ‘Sampled-data observer–based output–feedback fuzzy stabilization of nonlinear systems: exact discrete–time design approach’, Fuzzy Sets Syst., 2012, 201, (1), pp. 20–39.
    4. 4)
      • 26. Fridman, E.: ‘Descriptor discretized Lyapunov functional method: analysis and design’, IEEE Trans. Autom. Control., 2006, 51, (5), pp. 890–896.
    5. 5)
      • 8. Kim, H.J., Koo, G.B., Park, J.B., et al: ‘Decentralized sampled–data H∞ fuzzy filter for nonlinear large-scale systems’, Fuzzy Sets Syst., 2015, 273, (1), pp. 68–86.
    6. 6)
      • 17. Yoneyama, J.: ‘Robust H∞ filtering for sampled–data fuzzy systems’, Fuzzy Sets Syst., 2013, 217, (1), pp. 110–129.
    7. 7)
      • 27. Liu, K., Fridman, E.: ‘Wirtingers inequality and Lyapunov-based sampled-data stabilization’, Automatica, 2012, 48, (1), pp. 102–108.
    8. 8)
      • 15. Zhu, X.L., Wang, Y.: ‘Stabilization for sampled–data neural–network–based control systems’, IEEE Trans. Syst. Man Cybern. B, 2011, 41, (1), pp. 210–221.
    9. 9)
      • 6. Dong, H., Wang, Z., Gao, H.: ‘Distributed H∞ filtering for a class of Markovian jump nonlinear time–delay systems over lossy sensor networks’, IEEE Trans. Ind. Electron., 2013, 60, (10), pp. 4665–4672.
    10. 10)
      • 14. Gao, H., Sun, W., Shi, P.: ‘Robust sampled–data control for vehicle active suspension systems’, IEEE Trans. Control Syst. Technol., 2010, 18, (1), pp. 238–245.
    11. 11)
      • 9. Zhang, H., Shi, Y., Mehr, A.S.: ‘Robust weighted H∞ filtering for networked systems with intermittent measurements of multiple sensors’, Int. J. Adapt. Control Signal Process., 2011, 25, (4), pp. 313–330.
    12. 12)
      • 19. Kim, D.W., Lee, H.J., Tomizuka, M.: ‘Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach’, IEEE Trans. Fuzzy Syst., 2010, 18, (2), pp. 251–260.
    13. 13)
      • 31. Nguang, S.K.: ‘Comments on ‘fuzzy H (infinity) tracking control for nonlinear networked control systems in T–S fuzzy model’’, IEEE Trans. Syst. Man Cybern. B, 2010, 40, (3), p. 957.
    14. 14)
      • 13. Tanaka, K., Wang, H.O.: ‘Fuzzy control systems design and analysis: a linear matrix inequality approach’ (Wiley, New York, 2001).
    15. 15)
      • 25. Zhou, X.L., Wang, Y.: ‘Stabilization for sampled-data neural–network–based control systems’, IEEE Trans. Syst. Man Cybern. B, 2011, 41, (1), pp. 210–221.
    16. 16)
      • 23. Lam, H.K., Narimani, M.: ‘Stability analysis and performance design for fuzzy–model-based control system under imperfect premise matching’, IEEE Trans. Fuzzy Syst., 2009, 17, (4), pp. 949–961.
    17. 17)
      • 7. Zhang, H., Zhong, H., Dang, C.: ‘Delay-dependent decentralized filtering for discrete-time nonlinear interconnected systems with time–varying delay based on the T–S fuzzy model’, IEEE Trans. Fuzzy Syst., 2012, 20, (3), pp. 431–443.
    18. 18)
      • 16. Lam, H.K., Leung, F.H.: ‘Sampled–data fuzzy controller for time-delay nonlinear systems: fuzzy-model-based LMI approach’, IEEE Trans. Fuzzy Syst., 2007, 37, (3), pp. 617–629.
    19. 19)
      • 24. Wang, Z.P., Wu, H.N.: ‘On fuzzy sampled–data control of chaotic systems via a time–dependent Lyapunov functional approach’, IEEE Trans. Cybern., 2015, 45, (4), pp. 819–829.
    20. 20)
      • 21. Koo, G.B., Park, J.B., Joo, Y.H.: ‘Intelligent digital redesign for non–linear systems: observer–based sampled-data fuzzy control approach’, IET Control Theory Appl., 2015, 18, (2), pp. 251–260.
    21. 21)
      • 1. Su, X., Shi, P., Wu, L., et al: ‘A novel approach to filter design for T–S fuzzy discrete–time systems with time-varying delay’, IEEE Trans. Fuzzy Syst., 2012, 20, (6), pp. 1114–1129.
    22. 22)
      • 3. Noh, S.Y., Koo, G.B., Park, J.B., et al: ‘l∞ Fuzzy filter design for nonlinear systems with missing measurements: fuzzy basis-dependent Lyapunov function approach’, Int. J. Control Autom. Syst., 2016, 14, (2), pp. 425–434.
    23. 23)
      • 18. Ge, X., Han, Q.L., Jiang, X.: ‘Sampled-data H∞ filtering of Takagi–Sugeno fuzzy systems with interval time–varying delays’, J. Franklin Inst., 2014, 351, (1), pp. 2515–2542.
    24. 24)
      • 32. Chang, X.H.: ‘Robust nonfragile H∞ filtering of fuzzy systems with linear fractional parametric uncertainties’, IEEE Trans. Fuzzy Syst., 2012, 20, (6), pp. 1001–1011.
    25. 25)
      • 10. Lee, S.M., Ji, D.H., Kwon, O.M., et al: ‘Robust H∞ filtering for a class of discrete–time nonlinear systems’, Appl. Math. Comput., 2011, 217, (20), pp. 7991–7997.
    26. 26)
      • 28. Fang, C.H., Liu, Y.S., Kau, S.W., et al: ‘A new LMI-based approach to relaxed quadratic stabilization of T–S fuzzy control systems’, IEEE Trans. Fuzzy Syst., 2006, 14, (3), pp. 386–397.
    27. 27)
      • 5. Xu, S., Chen, T., Lam, J.: ‘Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time-delays’, IEEE Trans. Autom. Control, 2003, 48, (5), pp. 900–907.
    28. 28)
      • 2. Li, H., Pan, Y., Zhou, Q.: ‘Filter design for interval type–2 fuzzy systems with D stability constraints under a unified frame’, IEEE Trans. Fuzzy Syst., 2015, 23, (3), pp. 719–725.
    29. 29)
      • 29. Xie, X.P., Liu, Z.W., Zhu, X.L.: ‘An efficient approach for reducing the conservatism of LMI–based stability conditions for continuous-time T–S fuzzy systems’, Fuzzy Sets Syst., 2015, 263, (1), pp. 71–81.
    30. 30)
      • 22. Arino, C., Sala, A.: ‘Extensions to ‘stability analysis of fuzzy control systems subject to uncertain grades of membership’’, IEEE Trans. Syst. Man Cybern. B, 2008, 38, (2), pp. 558–563.
    31. 31)
      • 12. Chang, X.H., Yang, G.H.: ‘Nonfragile filter design for T–S fuzzy systems in standard form’, IEEE Trans. Ind. Electron., 2014, 61, (7), pp. 3448–3458.
    32. 32)
      • 11. Tian, E., Yue, D.: ‘Reliable H∞ filter design for T–S fuzzy model–based networked control systems with random sensor failure’, Int. J. Robust Nonlinear Control, 2013, 23, (1), pp. 15–32.
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