This study is concerned with observer-based fault estimation (FE) and fault-tolerant controller design for a class of discrete-time Takagi–Sugeno (T–S) fuzzy systems. There exist multiple time-varying state delays, sensor and actuator faults, local non-linear dynamics and exogenous disturbances in the systems. In comparison with the existing results, the approach suggested in this study is more flexible and feasible. By means of the n-step induction FE, a novel fuzzy adaptive descriptor observer is developed to obtain the n-step error functions. Then, an active dynamic output feedback fault-tolerant controller is designed to stabilise the closed-loop fuzzy system. Furthermore, a set of delay-dependent sufficient conditions are provided by the fuzzy Lyapunov function which utilises the form of linear matrix inequalities. The stability results from the observer and the controller in this study have less conservatism compared with the ones from the existence of observers and fault-tolerant controllers. At last, a simulation example is presented to demonstrate the advantages and effectiveness of the approach proposed in the study.

References

1. 1)
  - 24. Koenig, D.: ‘Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation’, IEEE Trans. Autom. Control, 2005, 50, (2), pp. 212–217.
2. 2)
  - 19. Menon, P.P., Edwards, C.: ‘A sliding mode observer for monitoring and fault estimation in a network of dynamical systems’, Int. J. Robust Nonlinear Control, 2014, 24, (17), pp. 2669–2685.
3. 3)
  - 33. Iwasaki, T., Hara, S.: ‘Generalized KYP lemma: unified frequency domain inequalities with design applications’, IEEE Trans. Autom. Control, 2005, 50, (1), pp. 41–59.
4. 4)
  - 23. Gao, Z., Ding, S.X.: ‘Fault estimation and fault-tolerant control for descriptor systems via proportional, multiple-integral and derivative observer design’, IET Control Theory Applic., 2007, 1, (5), pp. 1208–1218.
5. 5)
  - 22. Cao, S., Yi, Y., Guo, L.: ‘Anti-disturbance fault diagnosis for non-Gaussian stochastic distribution systems with multiple disturbances’, Neurocomputing, 2014, 136, (20), pp. 315–320.
6. 6)
  - 20. Sellami, A., Zanzouri, N.: ‘Diagnostic by Luenberger observer using bond graph approach for a photovoltaic system’. Green Energy Conversion Systems (GECS 2017), Hammamet, Tunisia, 2017.
7. 7)
  - 36. Nguang, S.K., Shi, P.: ‘H∞ fuzzy output feedback control design for nonlinear systems: an LMI approach’, IEEE Trans. Fuzzy Syst., 2003, 11, (3), pp. 331–340.
8. 8)
  - 39. Jiang, X., Han, Q.L.: ‘Robust H∞ control for uncertain Takagi–Sugeno fuzzy systems with interval time-varying delay’, IEEE Trans. Fuzzy Syst., 2007, 15, (2), pp. 321–331.
9. 9)
  - 11. Wang, Y., Zhang, H., Wang, X.: ‘Networked synchronization control of coupled dynamic networks with time-varying delay’, IEEE Trans. Cybern., 2010, 40, (6), pp. 1468–1479.
10. 10)
  - 28. Zhang, K., Jiang, B., Cocquempot, V.: ‘Fuzzy unknown input observer-based robust fault estimation design for discrete-time fuzzy systems’, Signal Process., 2016, 128, pp. 40–47.
11. 11)
  - 3. Wang, Y., Zheng, L., Zhang, H., et al: ‘Fuzzy observer-based repetitive tracking control for nonlinear systems’, IEEE Trans. Fuzzy Syst., 2019, pp. 1–1, DOI 10.1109/TFUZZ.2019.2936808.
12. 12)
  - 43. Cao, Y.Y., Frank, P.M.: ‘Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models’, Fuzzy Sets Syst., 2001, 124, (2), pp. 213–229.
13. 13)
  - 44. Li, J., Zhao, Y., Fen, Z., et al: ‘Reachable set estimation and dissipativity for discrete-time T–S fuzzy singular systems with time-varying delays’, Nonlinear Anal. Hybrid Syst., 2019, 31, pp. 166–179.
14. 14)
  - 8. Gao, Z., Zhou, Z., Qian, M.S., et al: ‘Active fault tolerant control scheme for satellite attitude system subject to actuator time-varying faults’, IET Control Theory Applic., 2018, 12, (3), pp. 405–412.
15. 15)
  - 6. Jiang, B., Zhang, K., Shi, P.: ‘Integrated fault estimation and accommodation design for discrete-time Takagi–Sugeno fuzzy systems with actuator faults’, IEEE Trans. Fuzzy Syst., 2011, 19, (2), pp. 291–304.
16. 16)
  - 1. Li, J., Zhang, Q., Yan, X., et al: ‘Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super-twisting algorithm’, IET Control Theory Applic., 2017, 11, (8), pp. 1134–1143.
17. 17)
  - 12. Zheng, W., Wang, H., Wang, H., et al: ‘Fuzzy dynamic output feedback control for T–S fuzzy discrete-time systems with multiple time-varying delays and unmatched disturbances’, IEEE Access, 2018, 6, pp. 31037–31049.
18. 18)
  - 25. Huang, S., Yang, G.: ‘Fault tolerant controller design for T–S fuzzy systems with time-varying delay and actuator faults: a k-step fault-estimation approach’, IEEE Trans. Fuzzy Syst., 2014, 22, (6), pp. 1526–1540.
19. 19)
  - 13. Sung, J.Y.: ‘Delay-independent fault detection and accommodation for non-linear strict-feedback systems with unknown time-varying delays’, IET Control Theory Applic., 2015, 9, (2), pp. 293–299.
20. 20)
  - 26. Gao, Z., Shi, X., Ding, S.X.: ‘Fuzzy state/disturbance observer design for T–S fuzzy systems with application to sensor fault estimation’, IEEE Trans. Cybern., 2008, 38, (3), pp. 875–880.
21. 21)
  - 18. Han, J., Liu, X., Wei, X., et al: ‘Reduced-order observer based fault estimation and fault-tolerant control for switched stochastic systems with actuator and sensor faults’, ISA Trans., 2019, 88, pp. 91–101.
22. 22)
  - 40. Garcia, G., Bernussou, J.: ‘Pole assignment for uncertain systems in a specified disk by state feedback’, ISA Trans., 1995, 40, (1), pp. 184–190.
23. 23)
  - 14. Fang, Y., Fei, J., Cao, D.: ‘Adaptive fuzzy-neural fractional-order current control of active power filter with finite-time sliding controller’, Int. J. Fuzzy Syst., 2019, 21, (5), pp. 1533–1543.
24. 24)
  - 17. Sun, S., Zhang, H., Wang, Y., et al: ‘Dynamic output feedback based fault-tolerant control design for T–S fuzzy systems with model uncertainties’, ISA Trans., 2018, 81, pp. 32–45.
25. 25)
  - 35. Boyd, S., Ghaoul, L.E., Feron, E., et al: ‘Linear matrix inequalities in system and control theory’ (SIAM, Philadelphia, PA, 1994).
26. 26)
  - 32. Lien, C.H., Yu, K.W., Lin, Y.F., et al: ‘Robust reliable H∞ control for uncertain nonlinear systems via LMI approach’, Appl. Math. Comput., 2008, 198, (1), pp. 453–462.
27. 27)
  - 15. Chu, Y., Fei, J., Hou, S.: ‘Adaptive global sliding-mode control for dynamic systems using double hidden layer recurrent neural network structure’, IEEE Trans. Neural Netw. Learn. Syst., 2020, 31, (4), pp. 1297–1309, DOI: 10.1109/TNNLS.2019.2919676 .
28. 28)
  - 42. Zhang, H., Wang, Y., Liu, D.: ‘Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays’, IEEE Trans. Cybern., 2008, 38, (1), pp. 126–140.
29. 29)
  - 9. Blanke, M., Kinnaert, M., Lunze, J., et al: ‘Diagnosis and fault-tolerant control’ (Springer, Berlin, Germany, 2006).
30. 30)
  - 31. Chen, J., Lin, C., Chen, B., et al: ‘Regularization and stabilization for rectangular T–S fuzzy discrete-time systems with time delay’, IEEE Trans. Syst. Man Cybern. Syst., 2019, 49, (4), pp. 833–842.
31. 31)
  - 37. Chen, C.: ‘Linear system theory and design’ (Oxford University Press, New York, America, 1999).
32. 32)
  - 34. Guan, X.P., Chen, C.L.: ‘Delay-dependent guaranteed cost control for T–S fuzzy systems with time delays’, IEEE Trans. Fuzzy Syst., 2004, 12, (2), pp. 236–249.
33. 33)
  - 27. Veluvolu, K.C., Soh, Y.C.: ‘High-gain observers with sliding mode for state and unknown input estimations’, IEEE Trans. Ind. Electron., 2009, 56, (9), pp. 3386–3393.
34. 34)
  - 21. Kamal, E., Aitouche, A., Abbes, D.: ‘Robust fuzzy scheduler fault tolerant control of wind energy systems subject to sensor and actuator faults’, Int. J. Electr. Power, 2014, 55, (2), pp. 402–419.
35. 35)
  - 2. Nasiri, A., Nguang, S.K., Swain, A., et al: ‘Robust output feedback controller design of discrete-time Takagi–Sugeno fuzzy systems: a non-monotonic Lyapunov approach’, IET Control Theory Applic., 2016, 10, (5), pp. 545–553.
36. 36)
  - 7. Yang, X., Wu, L., Lam H, K., et al: ‘Stability and stabilization of discrete-time T–S fuzzy systems with stochastic perturbation and time-varying delay’, IEEE Trans. Fuzzy Syst., 2014, 22, (1), pp. 124–138.
37. 37)
  - 30. Du, D., Cocquempot, V.: ‘Fault diagnosis and fault tolerant control for discrete-time linear systems with sensor fault’, IFAC-PapersOnLine, 2017, 50, (1), pp. 15754–15759.
38. 38)
  - 4. Liu, M., Cao, X., Shi, P.: ‘Fuzzy-model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults’, IEEE Trans. Fuzzy Syst., 2013, 21, (5), pp. 789–799.
39. 39)
  - 16. Zhu, Y., Fei, J.: ‘Disturbance observer based fuzzy sliding mode control of PV grid connected inverter’, IEEE Access, 2018, 6, pp. 21202–21211.
40. 40)
  - 29. Gao, H., Liu, X., Lam, J.: ‘Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay’, IEEE Trans. Cybern., 2009, 39, (2), pp. 306–317.
41. 41)
  - 38. Ahmadizadeh, S., Zarei, J., Karimi, H.R.: ‘A robust fault detection design for uncertain Takagi–Sugeno models with unknown inputs and time-varying delays’, Nonlinear Anal. Hybrid Syst., 2014, 11, pp. 98–117.
42. 42)
  - 5. Fei, Z., Shi, S., Wang, T., et al: ‘Improved stability criteria for discrete-time switched T–S fuzzy systems’, IEEE Trans. Syst. Man Cybern. Syst., 2018, pp. 1–9, DOI: 10.1109/TSMC.2018.2882630.
43. 43)
  - 10. Mao, Z., Jiang, B., Shi, P.: ‘Observer-based fault-tolerant control for a class of networked control systems with transfer delays’, J. Franklin Inst., 2011, 348, (4), pp. 763–776.
44. 44)
  - 41. Yuan, T., Shen, D., Wang Y, Q., et al: ‘Reliable H∞ control for uncertain nonlinear discrete-time systems subject to multiple internittent faults in sensors and/or actuators’, J. Franklin Inst., 2015, 352, (11), pp. 4721–4740.

Observer and fault-tolerant controller design for discrete-time multiple state-delayed T–S fuzzy systems

References

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